N. S. Ramm and A. S. Švarc :
“Geometriq blizosti, uniformnaq geometriq i topologiq ”
[Geometry of proximity, uniform geometry and topology ],
Mat. Sb., Nov. Ser.
33(75) : 1
(1953 ),
pp. 157–180 .
MR
61368
Zbl
0050.39101
article
People
BibTeX
@article {key61368m,
AUTHOR = {Ramm, N. S. and \v{S}varc, A. S.},
TITLE = {Geometriq blizosti, uniformnaq geometriq
i topologiq [Geometry of proximity,
uniform geometry and topology]},
JOURNAL = {Mat. Sb., Nov. Ser.},
FJOURNAL = {Matematicheski\u{\i} Sbornik. Novaya
Seriya},
VOLUME = {33(75)},
NUMBER = {1},
YEAR = {1953},
PAGES = {157--180},
URL = {http://mi.mathnet.ru/msb5339},
NOTE = {MR:61368. Zbl:0050.39101.},
ISSN = {0368-8666},
}
A. S. Švarc :
“Homologies of the spinor group ,”
Dokl. Akad. Nauk SSSR
104
(1955 ),
pp. 26–29 .
MR
74829
Zbl
0068.37002
article
BibTeX
@article {key74829m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Homologies of the spinor group},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {104},
YEAR = {1955},
PAGES = {26--29},
NOTE = {MR:74829. Zbl:0068.37002.},
ISSN = {0002-3264},
}
A. S. Švarc :
“On the metric order of closed sets in Euclidean space ”
[O metricheskom porqdke zamknutjx mnozhestv ävklidova prostranstva ],
Mat. Sb., Nov. Ser.
36(78) : 2
(1955 ),
pp. 263–270 .
MR
70170
Zbl
0064.17002
article
BibTeX
@article {key70170m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {On the metric order of closed sets in
{E}uclidean space [O metricheskom porqdke
zamknutjx mnozhestv \"avklidova prostranstva]},
JOURNAL = {Mat. Sb., Nov. Ser.},
FJOURNAL = {Matematicheski\u{\i} Sbornik. Novaya
Seriya},
VOLUME = {36(78)},
NUMBER = {2},
YEAR = {1955},
PAGES = {263--270},
URL = {http://mi.mathnet.ru/msb5190},
NOTE = {MR:70170. Zbl:0064.17002.},
ISSN = {0368-8666},
}
A. S. Schwarz :
“A volume invariant of coverings ,”
Doklady Akad. Nauk SSSR
105
(1955 ),
pp. 32–34 .
In Russian.
Zbl
0066.15903
article
BibTeX
@article {key0066.15903z,
AUTHOR = {Schwarz, A. S.},
TITLE = {A volume invariant of coverings},
JOURNAL = {Doklady Akad. Nauk SSSR},
VOLUME = {105},
YEAR = {1955},
PAGES = {32--34},
NOTE = {In Russian. Zbl:0066.15903.},
}
A. S. Švarc :
“Gomologii prostranstv zamknutjx krivjx ”
[Homology of spaces of closed curves ],
Dokl. Akad. Nauk SSSR
117 : 5
(1957 ),
pp. 769–772 .
MR
100874
Zbl
0079.17003
article
BibTeX
@article {key100874m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Gomologii prostranstv zamknutjx krivjx
[Homology of spaces of closed curves]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {117},
NUMBER = {5},
YEAR = {1957},
PAGES = {769--772},
URL = {http://mi.mathnet.ru/dan22580},
NOTE = {MR:100874. Zbl:0079.17003.},
ISSN = {0002-3264},
}
V. A. Rohlin and A. S. Švarc :
“O kombinatornoy invariantnosti klassov Pontrqgina ”
[On the combinatorial invariance of the Pontryagin classes ],
Dokl. Akad. Nauk SSSR
114 : 3
(1957 ),
pp. 490–493 .
MR
102070
Zbl
0078.36803
article
People
BibTeX
Vladimir Abramovich Rokhlin
Related
@article {key102070m,
AUTHOR = {Rohlin, V. A. and \v{S}varc, A. S.},
TITLE = {O kombinatornoy invariantnosti klassov
{P}ontrqgina [On the combinatorial invariance
of the {P}ontryagin classes]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {114},
NUMBER = {3},
YEAR = {1957},
PAGES = {490--493},
URL = {http://mi.mathnet.ru/dan21973},
NOTE = {MR:102070. Zbl:0078.36803.},
ISSN = {0002-3264},
}
A. S. Švarc :
“On a problem of Sikorskiĭ ”
[K odnoy zadache Sikorskogo ],
Uspekhi Mat. Nauk
12 : 4(76)
(1957 ),
pp. 215 .
MR
89397
Zbl
0078.14904
article
BibTeX
@article {key89397m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {On a problem of Sikorski\u{\i} [K odnoy
zadache {S}ikorskogo]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {12},
NUMBER = {4(76)},
YEAR = {1957},
PAGES = {215},
URL = {http://mi.mathnet.ru/umn7677},
NOTE = {MR:89397. Zbl:0078.14904.},
ISSN = {0042-1316},
}
A. S. Švarc :
“Nekotorje ocenki roda topologicheskogo prostranstva v smjsle Krasnosel’skogo ”
[Some estimates of the genus of a topological space in the sense of Krasnosel’skiĭ ],
Uspekhi Mat. Nauk
12 : 4(76)
(1957 ),
pp. 209–214 .
MR
90055
Zbl
0078.36402
article
BibTeX
@article {key90055m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Nekotorje ocenki roda topologicheskogo
prostranstva v smjsle {K}rasnosel\cprime
skogo [Some estimates of the genus of
a topological space in the sense of
{K}rasnosel\cprime ski\u{\i}]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {12},
NUMBER = {4(76)},
YEAR = {1957},
PAGES = {209--214},
URL = {http://mi.mathnet.ru/umn7676},
NOTE = {MR:90055. Zbl:0078.36402.},
ISSN = {0042-1316},
}
A. S. Švarc :
“Rod rassloennogo prostranstva ”
[The genus of a fiber space ],
Dokl. Akad. Nauk SSSR
119 : 2
(1958 ),
pp. 219–222 .
MR
102812
Zbl
0085.37703
article
BibTeX
@article {key102812m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Rod rassloennogo prostranstva [The genus
of a fiber space]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {119},
NUMBER = {2},
YEAR = {1958},
PAGES = {219--222},
URL = {http://mi.mathnet.ru/dan22829},
NOTE = {MR:102812. Zbl:0085.37703.},
ISSN = {0002-3264},
}
A. S. Švarc :
“O geodezicheskix dugax na rimanovjx mnogoobraziqx ”
[Geodesic arcs on Riemann manifolds ],
Uspekhi Mat. Nauk
13 : 6(84)
(1958 ),
pp. 181–184 .
MR
102076
Zbl
0086.36302
article
BibTeX
@article {key102076m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {O geodezicheskix dugax na rimanovjx
mnogoobraziqx [Geodesic arcs on {R}iemann
manifolds]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {13},
NUMBER = {6(84)},
YEAR = {1958},
PAGES = {181--184},
URL = {http://mi.mathnet.ru/umn7513},
NOTE = {MR:102076. Zbl:0086.36302.},
ISSN = {0042-1316},
}
A. S. Schwarz :
“On the genus of a fiber space ,”
Doklady Akad. Nauk SSSR
126
(1959 ),
pp. 719–722 .
In Russian.
Zbl
0087.38204
article
BibTeX
@article {key0087.38204z,
AUTHOR = {Schwarz, A. S.},
TITLE = {On the genus of a fiber space},
JOURNAL = {Doklady Akad. Nauk SSSR},
VOLUME = {126},
YEAR = {1959},
PAGES = {719--722},
NOTE = {In Russian. Zbl:0087.38204.},
}
A. S. Švarc :
“Gomologii prostranstv zamknutjx krivjx ”
[Homology of spaces of closed curves ],
Tr. Mosk. Mat. O.-va
9
(1960 ),
pp. 3–44 .
MR
133824
Zbl
0115.17001
article
BibTeX
@article {key133824m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Gomologii prostranstv zamknutjx krivjx
[Homology of spaces of closed curves]},
JOURNAL = {Tr. Mosk. Mat. O.-va},
FJOURNAL = {Trudy Moskovskogo Matematicheskogo Obshchestva},
VOLUME = {9},
YEAR = {1960},
PAGES = {3--44},
URL = {http://mi.mathnet.ru/mmo95},
NOTE = {MR:133824. Zbl:0115.17001.},
ISSN = {0134-8663},
}
A. S. Shvarts :
“Stability of stationary values ,”
Sov. Math., Dokl.
1
(1960 ),
pp. 439–441 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 131 :6 (1960) .
Zbl
0094.08203
article
BibTeX
@article {key0094.08203z,
AUTHOR = {Shvarts, A. S.},
TITLE = {Stability of stationary values},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {1},
YEAR = {1960},
PAGES = {439--441},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{131}:6 (1960). Zbl:0094.08203.},
ISSN = {0197-6788},
}
A. S. Švarc :
“Ustoychivost’stacionarnjx znacheniy ”
[Stability of stationary values ],
Dokl. Akad. Nauk SSSR
131 : 6
(1960 ),
pp. 1276–1278 .
An English translation was published in Sov. Math., Dokl. 1 (1960) .
MR
163329
article
BibTeX
@article {key163329m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Ustoychivost\cprime stacionarnjx znacheniy
[Stability of stationary values]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {131},
NUMBER = {6},
YEAR = {1960},
PAGES = {1276--1278},
URL = {http://mi.mathnet.ru/dan40025},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{1}
(1960). MR:163329.},
ISSN = {0002-3264},
}
A. S. Švarc :
“K gomotopicheskoy teorii rassloennjx prostranstv ”
[On the homotopy theory of fiber spaces ],
Dokl. Akad. Nauk SSSR
141 : 1
(1961 ),
pp. 51–54 .
An English translation was published in Sov. Math., Dokl. 2 (1961) .
MR
142124
article
BibTeX
@article {key142124m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {K gomotopicheskoy teorii rassloennjx
prostranstv [On the homotopy theory
of fiber spaces]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {141},
NUMBER = {1},
YEAR = {1961},
PAGES = {51--54},
URL = {http://mi.mathnet.ru/dan25709},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{2}
(1961). MR:142124.},
ISSN = {0002-3264},
}
A. S. Švarc :
“O nekotorjx ponqtiqx, svqzannjx s ponqtiem roda rassloennogo prostranstva ”
[On some concepts related to the concept of the genus of a fibre space ],
Dokl. Akad. Nauk SSSR
136 : 2
(1961 ),
pp. 301–303 .
An English translation was published in Sov. Math., Dokl. 2 (1961) .
MR
131879
Zbl
0096.37705
article
BibTeX
@article {key131879m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {O nekotorjx ponqtiqx, svqzannjx s ponqtiem
roda rassloennogo prostranstva [On some
concepts related to the concept of the
genus of a fibre space]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {136},
NUMBER = {2},
YEAR = {1961},
PAGES = {301--303},
URL = {http://mi.mathnet.ru/dan24503},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{2}
(1961). MR:131879. Zbl:0096.37705.},
ISSN = {0002-3264},
}
A. S. Švarc :
“Gomotopicheskaq dvoystvennost’dlq prostranstva s gruppoy operatorov ”
[Homotopy duality for a space with a group of operators ],
Dokl. Akad. Nauk SSSR
136 : 1
(1961 ),
pp. 43–46 .
An English translation was published in Sov. Math., Dokl. 2 (1961) .
MR
132547
article
BibTeX
@article {key132547m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Gomotopicheskaq dvoystvennost\cprime
dlq prostranstva s gruppoy operatorov
[Homotopy duality for a space with a
group of operators]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {136},
NUMBER = {1},
YEAR = {1961},
PAGES = {43--46},
URL = {http://mi.mathnet.ru/dan24462},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{2}
(1961). MR:132547.},
ISSN = {0002-3264},
}
A. S. Švarc :
“Rod rassloennogo prostranstva ”
[The genus of a fibre space ],
Tr. Mosk. Mat. O.-va
10
(1961 ),
pp. 217–272 .
An English translation was published in Am. Math. Soc. Transl., Ser. 2 55 (1966) ,.
MR
154284
article
BibTeX
@article {key154284m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Rod rassloennogo prostranstva [The genus
of a fibre space]},
JOURNAL = {Tr. Mosk. Mat. O.-va},
FJOURNAL = {Trudy Moskovskogo Matematicheskogo Obshchestva},
VOLUME = {10},
YEAR = {1961},
PAGES = {217--272},
URL = {http://mi.mathnet.ru/mmo120},
NOTE = {An English translation was published
in \textit{Am. Math. Soc. Transl., Ser.
2} \textbf{55} (1966),. MR:154284.},
ISSN = {0134-8663},
}
A. S. Shvarts :
“Homotopic duality for spaces with a group of operators ,”
Sov. Math., Dokl.
2
(1961 ),
pp. 32–35 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 136 :1 (1961) .
Zbl
0096.37704
article
BibTeX
@article {key0096.37704z,
AUTHOR = {Shvarts, A. S.},
TITLE = {Homotopic duality for spaces with a
group of operators},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {2},
YEAR = {1961},
PAGES = {32--35},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{136}:1 (1961). Zbl:0096.37704.},
ISSN = {0197-6788},
}
A. S. Shvarts :
“On the homotopy theory of fiber spaces ,”
Sov. Math., Dokl.
2
(1961 ),
pp. 1405–1408 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 141 :1 (1961) .
Zbl
0113.17102
article
BibTeX
@article {key0113.17102z,
AUTHOR = {Shvarts, A. S.},
TITLE = {On the homotopy theory of fiber spaces},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {2},
YEAR = {1961},
PAGES = {1405--1408},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{141}:1 (1961). Zbl:0113.17102.},
ISSN = {0197-6788},
}
D. B. Fuks and A. S. Švarc :
“K gomotopicheskoy teorii funktorov v kategorii topologicheskix prostranstv ”
[On the homotopy theory of functors in the category of topological spaces ],
Dokl. Akad. Nauk SSSR
143 : 3
(1962 ),
pp. 543–546 .
An English translation was published in Sov. Math., Dokl. 3 (1962) .
MR
137116
article
People
BibTeX
@article {key137116m,
AUTHOR = {Fuks, D. B. and \v{S}varc, A. S.},
TITLE = {K gomotopicheskoy teorii funktorov v
kategorii topologicheskix prostranstv
[On the homotopy theory of functors
in the category of topological spaces]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {143},
NUMBER = {3},
YEAR = {1962},
PAGES = {543--546},
URL = {http://mi.mathnet.ru/dan26268},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{3}
(1962). MR:137116.},
ISSN = {0002-3264},
}
A. S. Švarc :
“Rod rassloennogo prostranstva ”
[The genus of a fibre space ],
Tr. Mosk. Mat. O.-va
11
(1962 ),
pp. 99–126 .
An English translation was published in Am. Math. Soc. Transl., Ser. 2 55 (1966) ,.
MR
151982
article
BibTeX
@article {key151982m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Rod rassloennogo prostranstva [The genus
of a fibre space]},
JOURNAL = {Tr. Mosk. Mat. O.-va},
FJOURNAL = {Trudy Moskovskogo Matematicheskogo Obshchestva},
VOLUME = {11},
YEAR = {1962},
PAGES = {99--126},
URL = {http://mi.mathnet.ru/mmo132},
NOTE = {An English translation was published
in \textit{Am. Math. Soc. Transl., Ser.
2} \textbf{55} (1966),. MR:151982.},
ISSN = {0134-8663},
}
D. B. Fuks and A. S. Shvarts :
“On the homotopy theory of functors in the category of topological spaces ,”
Sov. Math., Dokl.
3
(1962 ),
pp. 444–447 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 143 :3 (1962) .
Zbl
0126.18504
article
People
BibTeX
@article {key0126.18504z,
AUTHOR = {Fuks, D. B. and Shvarts, A. S.},
TITLE = {On the homotopy theory of functors in
the category of topological spaces},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {3},
YEAR = {1962},
PAGES = {444--447},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{143}:3 (1962). Zbl:0126.18504.},
ISSN = {0197-6788},
}
A. S. Švarc :
“Funktorj v kategoriqx banaxovjx prostranstv ”
[Functors in the categories of Banach spaces ],
Dokl. Akad. Nauk SSSR
149 : 1
(1963 ),
pp. 44–47 .
An English translation was published in Sov. Math., Dokl. 4 (1963) .
MR
154087
article
BibTeX
@article {key154087m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Funktorj v kategoriqx banaxovjx prostranstv
[Functors in the categories of {B}anach
spaces]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {149},
NUMBER = {1},
YEAR = {1963},
PAGES = {44--47},
URL = {http://mi.mathnet.ru/dan27662},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{4}
(1963). MR:154087.},
ISSN = {0002-3264},
}
A. S. Švarc :
“Dvoystvennost’funktorov ”
[Duality of functors ],
Dokl. Akad. Nauk SSSR
148 : 2
(1963 ),
pp. 288–291 .
An English translation was published in Sov. Math., Dokl. 4 (1963) .
MR
168629
article
BibTeX
@article {key168629m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Dvoystvennost\cprime funktorov [Duality
of functors]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {148},
NUMBER = {2},
YEAR = {1963},
PAGES = {288--291},
URL = {http://mi.mathnet.ru/dan27464},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{4}
(1963). MR:168629.},
ISSN = {0002-3264},
}
A. S. Shvarts :
“Functors in Banach space categories ,”
Sov. Math., Dokl.
4
(1963 ),
pp. 317–320 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 149 :1 (1963) .
Zbl
0124.06601
article
BibTeX
@article {key0124.06601z,
AUTHOR = {Shvarts, A. S.},
TITLE = {Functors in {B}anach space categories},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {4},
YEAR = {1963},
PAGES = {317--320},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{149}:1 (1963). Zbl:0124.06601.},
ISSN = {0197-6788},
}
A. S. Shvarts :
“Duality of functors ,”
Sov. Math., Dokl.
4
(1963 ),
pp. 89–92 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 148 :2 (1963) .
Zbl
0168.26803
article
BibTeX
@article {key0168.26803z,
AUTHOR = {Shvarts, A. S.},
TITLE = {Duality of functors},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {4},
YEAR = {1963},
PAGES = {89--92},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{148}:2 (1963). Zbl:0168.26803.},
ISSN = {0197-6788},
}
A. S. Švarc :
“K gomotopicheskoy topologii banaxovjx prostranstv ”
[On the homotopic topology of Banach spaces ],
Dokl. Akad. Nauk SSSR
154 : 1
(1964 ),
pp. 61–63 .
An English translation was published in Sov. Math., Dokl. 5 (1964) .
MR
160095
article
BibTeX
@article {key160095m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {K gomotopicheskoy topologii banaxovjx
prostranstv [On the homotopic topology
of {B}anach spaces]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {154},
NUMBER = {1},
YEAR = {1964},
PAGES = {61--63},
URL = {http://mi.mathnet.ru/dan28985},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{5}
(1964). MR:160095.},
ISSN = {0002-3264},
}
B. S. Mityagin and A. S. Shvarts :
“Functors in categories of Banach spaces ”
[Funktorj v kategoriqx banaxovjx prostranstv ],
Uspekhi Mat. Nauk
19 : 2(116)
(1964 ),
pp. 65–130 .
An English translation was published in Russ. Math. Surv. 19 :2 (1964) .
MR
166593
article
People
BibTeX
@article {key166593m,
AUTHOR = {Mityagin, B. S. and Shvarts, A. S.},
TITLE = {Functors in categories of {B}anach spaces
[Funktorj v kategoriqx banaxovjx prostranstv]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {19},
NUMBER = {2(116)},
YEAR = {1964},
PAGES = {65--130},
URL = {http://mi.mathnet.ru/umn6188},
NOTE = {An English translation was published
in \textit{Russ. Math. Surv.} \textbf{19}:2
(1964). MR:166593.},
ISSN = {0042-1316},
}
B. S. Mityagin and A. S. Shvarts :
“Functors in categories of Banach spaces ,”
Russ. Math. Surv.
19 : 2
(April 1964 ),
pp. 65–127 .
English translation of Russian original published in Uspekhi Mat. Nauk 19 :2(116) (1964) .
Zbl
0129.08205
article
People
BibTeX
@article {key0129.08205z,
AUTHOR = {Mityagin, B. S. and Shvarts, A. S.},
TITLE = {Functors in categories of {B}anach spaces},
JOURNAL = {Russ. Math. Surv.},
FJOURNAL = {Russian Mathematical Surveys},
VOLUME = {19},
NUMBER = {2},
MONTH = {April},
YEAR = {1964},
PAGES = {65--127},
DOI = {10.1070/RM1964v019n02ABEH001146},
NOTE = {English translation of Russian original
published in \textit{Uspekhi Mat. Nauk}
\textbf{19}:2(116) (1964). Zbl:0129.08205.},
ISSN = {0036-0279},
}
A. S. Shvarts :
“The homotopic topology of Banach spaces ,”
Sov. Math., Dokl.
5
(1964 ),
pp. 57–59 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 154 :1 (1964) .
Zbl
0181.39904
article
BibTeX
@article {key0181.39904z,
AUTHOR = {Shvarts, A. S.},
TITLE = {The homotopic topology of {B}anach spaces},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {5},
YEAR = {1964},
PAGES = {57--59},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{154}:1 (1964). Zbl:0181.39904.},
ISSN = {0197-6788},
}
L. M. Kissina and A. S. Švarc :
“K voprosu ob opisanii dvoystvennogo funktora ”
[On the question of description of the duality functor ],
Dokl. Akad. Nauk SSSR
167 : 2
(1966 ),
pp. 282–285 .
MR
219065
article
People
BibTeX
@article {key219065m,
AUTHOR = {Kissina, L. M. and \v{S}varc, A. S.},
TITLE = {K voprosu ob opisanii dvoystvennogo
funktora [On the question of description
of the duality functor]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {167},
NUMBER = {2},
YEAR = {1966},
PAGES = {282--285},
URL = {http://mi.mathnet.ru/dan32145},
NOTE = {MR:219065.},
ISSN = {0002-3264},
}
A. S. Švarc :
“Gomologii prostranstv gladkix vlozheniy ”
[Homology of spaces of smooth embeddings ],
Dokl. Akad. Nauk SSSR
167 : 1
(1966 ),
pp. 41–44 .
An English translation was published in Sov. Math., Dokl. 7 (1966) .
MR
208612
article
BibTeX
@article {key208612m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Gomologii prostranstv gladkix vlozheniy
[Homology of spaces of smooth embeddings]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {167},
NUMBER = {1},
YEAR = {1966},
PAGES = {41--44},
URL = {http://mi.mathnet.ru/dan32127},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{7}
(1966). MR:208612.},
ISSN = {0002-3264},
}
R. S. Pokazeeva and A. S. Švarc :
“Dvoystvennost’funktorov ”
[Duality of functors ],
Mat. Sb., Nov. Ser.
71(113) : 3
(1966 ),
pp. 357–385 .
An English translation was published Am. Math. Soc., Translat., II. Ser. 73 (1968) .
MR
220650
article
People
BibTeX
@article {key220650m,
AUTHOR = {Pokazeeva, R. S. and \v{S}varc, A. S.},
TITLE = {Dvoystvennost\cprime funktorov [Duality
of functors]},
JOURNAL = {Mat. Sb., Nov. Ser.},
FJOURNAL = {Matematicheski\u{\i} Sbornik. Novaya
Seriya},
VOLUME = {71(113)},
NUMBER = {3},
YEAR = {1966},
PAGES = {357--385},
URL = {http://mi.mathnet.ru/msb4270},
NOTE = {An English translation was published
\textit{Am. Math. Soc., Translat., II.
Ser.} \textbf{73} (1968). MR:220650.},
ISSN = {0368-8666},
}
A. S. Shvarts :
“Homology of spaces of smooth embeddings ,”
Sov. Math., Dokl.
7
(1966 ),
pp. 339–342 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 167 :1 (1966) .
Zbl
0149.20702
article
BibTeX
@article {key0149.20702z,
AUTHOR = {Shvarts, A. S.},
TITLE = {Homology of spaces of smooth embeddings},
JOURNAL = {Sov. Math., Dokl.},
FJOURNAL = {Soviet Mathematics. Doklady},
VOLUME = {7},
YEAR = {1966},
PAGES = {339--342},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{167}:1 (1966). Zbl:0149.20702.},
ISSN = {0197-6788},
}
A. S. Shvarts :
“The genus of a fiber space, I, II ,”
pp. 49–140
in
Eleven papers on topology and algebra .
American Mathematical Society Translations. Series 2 55 .
1966 .
English translation of two-part Russian original published in Tr. Mosk. Mat. O.-va 19 (1961) and Tr. Mosk. Mat. O.-va 11 (1962) .
Zbl
0178.26202
incollection
BibTeX
@incollection {key0178.26202z,
AUTHOR = {Shvarts, A. S.},
TITLE = {The genus of a fiber space, {I}, {II}},
BOOKTITLE = {Eleven papers on topology and algebra},
SERIES = {American Mathematical Society Translations.
Series 2},
NUMBER = {55},
YEAR = {1966},
PAGES = {49--140},
NOTE = {English translation of two-part Russian
original published in \textit{Tr. Mosk.
Mat. O.-va} \textbf{19} (1961) and \textit{Tr.
Mosk. Mat. O.-va} \textbf{11} (1962).
Zbl:0178.26202.},
ISSN = {0065-9290},
ISBN = {9780821817551},
}
V. V. Kuznecov and A. S. Švarc :
“Dvoystvennost’funktorov i dvoystvennost’kategoriy ”
[Duality of functors and duality of categories ],
Uspekhi Mat. Nauk
22 : 1(133)
(1967 ),
pp. 168–170 .
MR
204491
article
People
BibTeX
Vladimir Vasilyevich Kuznetsov
Related
@article {key204491m,
AUTHOR = {Kuznecov, V. V. and \v{S}varc, A. S.},
TITLE = {Dvoystvennost\cprime funktorov i dvoystvennost\cprime
kategoriy [Duality of functors and duality
of categories]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {22},
NUMBER = {1(133)},
YEAR = {1967},
PAGES = {168--170},
URL = {http://mi.mathnet.ru/umn5707},
NOTE = {MR:204491.},
ISSN = {0042-1316},
}
A. S. Shvarts :
“Novaq formulirovka kvantovoy teorii ”
[A new formulation of quantum theory ],
Dokl. Akad. Nauk SSSR
173 : 4
(1967 ),
pp. 793–796 .
article
BibTeX
@article {key38240828,
AUTHOR = {Shvarts, A. S.},
TITLE = {Novaq formulirovka kvantovoy teorii
[A new formulation of quantum theory]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {173},
NUMBER = {4},
YEAR = {1967},
PAGES = {793--796},
URL = {http://mi.mathnet.ru/dan32994},
ISSN = {0002-3264},
}
A. S. Schwarz :
“A new formulation of the quantum theory ,”
Dokl. Akad. Nauk SSSR
173 : 4
(1967 ),
pp. 793–796 .
In Russian.
article
BibTeX
@article {key56644431,
AUTHOR = {Schwarz, A. S.},
TITLE = {A new formulation of the quantum theory},
JOURNAL = {Dokl. Akad. Nauk SSSR},
VOLUME = {173},
NUMBER = {4},
YEAR = {1967},
PAGES = {793--796},
URL = {http://mi.mathnet.ru/dan32994},
NOTE = {In Russian.},
}
V. V. Kuznetsov and A. S. Shvarts :
“Duality of functors and duality of categories ,”
Siberian Math. J.
9 : 4
(July 1968 ),
pp. 627–636 .
English translation of Russian original published in Sib. Mat. Zh. 9 :4 (1968) .
article
Abstract
People
BibTeX
Vladimir Vasilyevich Kuznetsov
Related
@article {key68649354,
AUTHOR = {Kuznetsov, V. V. and Shvarts, A. S.},
TITLE = {Duality of functors and duality of categories},
JOURNAL = {Siberian Math. J.},
FJOURNAL = {Siberian Mathematical Journal},
VOLUME = {9},
NUMBER = {4},
MONTH = {July},
YEAR = {1968},
PAGES = {627--636},
DOI = {10.1007/BF02199098},
NOTE = {English translation of Russian original
published in \textit{Sib. Mat. Zh.}
\textbf{9}:4 (1968).},
ISSN = {0037-4466},
}
V. V. Kuznecov and A. S. Švarc :
“Dvoystvennost’funktorov i dvoystvennost’kategoriy ”
[Duality of functors and duality of categories ],
Sib. Mat. Zh.
9 : 4
(1968 ),
pp. 840–856 .
An English translation was published in Siberian Math. J. 9 :4 (1968) .
MR
236241
Zbl
0186.03002
article
People
BibTeX
Vladimir Vasilyevich Kuznetsov
Related
@article {key236241m,
AUTHOR = {Kuznecov, V. V. and \v{S}varc, A. S.},
TITLE = {Dvoystvennost\cprime funktorov i dvoystvennost\cprime
kategoriy [Duality of functors and duality
of categories]},
JOURNAL = {Sib. Mat. Zh.},
FJOURNAL = {Sibirski\u{\i} Matematicheski\u{\i}
Zhurnal},
VOLUME = {9},
NUMBER = {4},
YEAR = {1968},
PAGES = {840--856},
URL = {http://mi.mathnet.ru/eng/smj5570},
NOTE = {An English translation was published
in \textit{Siberian Math. J.} \textbf{9}:4
(1968). MR:236241. Zbl:0186.03002.},
}
A. S. Shvarts :
“O postanovke zadach statisticheskoy fiziki ”
[On the statement of problems in statistical physics ],
Uspekhi Mat. Nauk
23 : 2(140)
(1968 ),
pp. 217–218 .
article
BibTeX
@article {key34758449,
AUTHOR = {Shvarts, A. S.},
TITLE = {O postanovke zadach statisticheskoy
fiziki [On the statement of problems
in statistical physics]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {23},
NUMBER = {2(140)},
YEAR = {1968},
PAGES = {217--218},
URL = {http://mi.mathnet.ru/umn5620},
ISSN = {0042-1316},
}
R. S. Pokazeeva and A. S. Švarc :
“Duality of functors ,”
pp. 1–35
in
Fourteen papers on algebra, topology, algebraic and differential geometry .
American Mathematical Society Translations. Series 2 73 .
1968 .
English translation of Russian original published Mat. Sb. 71(113) :3 (1966) .
Zbl
0208.02803
incollection
People
BibTeX
@incollection {key0208.02803z,
AUTHOR = {Pokazeeva, R. S. and \v{S}varc, A. S.},
TITLE = {Duality of functors},
BOOKTITLE = {Fourteen papers on algebra, topology,
algebraic and differential geometry},
SERIES = {American Mathematical Society Translations.
Series 2},
NUMBER = {73},
YEAR = {1968},
PAGES = {1--35},
URL = {https://www.ams.org/books/trans2/073/01/trans2073-01.pdf},
NOTE = {English translation of Russian original
published \textit{Mat. Sb.} \textbf{71(113)}:3
(1966). Zbl:0208.02803.},
ISSN = {0065-9290},
ISBN = {9780821817735},
}
Yu. S. Tyupkin and A. S. Schwartz :
“Zadachi statisticheskoy fiziki v sil’no vjtqnutjx telax ”
[Problems of statistical physics in strongly prolate bodies ],
Dokl. Akad. Nauk SSSR
185 : 2
(1969 ),
pp. 299–301 .
article
People
BibTeX
@article {key12050556,
AUTHOR = {Tyupkin, Yu. S. and Schwartz, A. S.},
TITLE = {Zadachi statisticheskoy fiziki v sil'no
vjtqnutjx telax [Problems of statistical
physics in strongly prolate bodies]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {185},
NUMBER = {2},
YEAR = {1969},
PAGES = {299--301},
URL = {http://mi.mathnet.ru/dan34503},
ISSN = {0002-3264},
}
V. N. Likhachev, Yu. S. Tyupkin, and A. S. Shvarts :
“The adiabatic \( S \) -matrix and quasiparticles ,”
Theoret. and Math. Phys.
2 : 1
(January 1970 ),
pp. 1–20 .
English translation of Russian original published in Teor. Mat. Fiz. 2 :1 (1970) .
article
Abstract
People
BibTeX
@article {key74457568,
AUTHOR = {Likhachev, V. N. and Tyupkin, Yu. S.
and Shvarts, A. S.},
TITLE = {The adiabatic \$S\$-matrix and quasiparticles},
JOURNAL = {Theoret. and Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {2},
NUMBER = {1},
MONTH = {January},
YEAR = {1970},
PAGES = {1--20},
DOI = {10.1007/BF01028851},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{2}:1 (1970).},
ISSN = {0040-5779},
}
V. N. Likhachev, Yu. S. Tyupkin, and A. S. Schwartz :
“Adiabaticheskaq \( S \) -matrica i kvazichasticj ”
[Adiabatic \( S \) -matrix and quasiparticles ],
Teor. Mat. Fiz.
2 : 1
(1970 ),
pp. 3–29 .
An English translation was published in Theoret. and Math. Phys. 2 :1 (1970) .
article
People
BibTeX
@article {key90619781,
AUTHOR = {Likhachev, V. N. and Tyupkin, Yu. S.
and Schwartz, A. S.},
TITLE = {Adiabaticheskaq \$S\$-matrica i kvazichasticj
[Adiabatic \$S\$-matrix and quasiparticles]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {2},
NUMBER = {1},
YEAR = {1970},
PAGES = {3--29},
URL = {http://mi.mathnet.ru/tmf3985},
NOTE = {An English translation was published
in \textit{Theoret. and Math. Phys.}
\textbf{2}:1 (1970).},
ISSN = {0564-6162},
}
A. S. Švarc :
“O postanovke zadach statisticheskoy fiziki ”
[On the statement of problems in statistical physics ],
Tr. Mosk. Mat. O.-va
22
(1970 ),
pp. 127–160 .
MR
353876
article
BibTeX
@article {key353876m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {O postanovke zadach statisticheskoy
fiziki [On the statement of problems
in statistical physics]},
JOURNAL = {Tr. Mosk. Mat. O.-va},
FJOURNAL = {Trudy Moskovskogo Matematicheskogo Obshchestva},
VOLUME = {22},
YEAR = {1970},
PAGES = {127--160},
URL = {http://mi.mathnet.ru/mmo234},
NOTE = {MR:353876.},
ISSN = {0134-8663},
}
V. V. Kuznecov and A. S. Švarc :
“Funktorj v kategorii vektornjx prostranstv ”
[Functors in the category of vector spaces ],
Dokl. Akad. Nauk SSSR
196 : 1
(1971 ),
pp. 40–43 .
An English translation was published in Sov. Math., Dokl. 12 (1971) .
MR
272855
article
People
BibTeX
Vladimir Vasilyevich Kuznetsov
Related
@article {key272855m,
AUTHOR = {Kuznecov, V. V. and \v{S}varc, A. S.},
TITLE = {Funktorj v kategorii vektornjx prostranstv
[Functors in the category of vector
spaces]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {196},
NUMBER = {1},
YEAR = {1971},
PAGES = {40--43},
URL = {http://mi.mathnet.ru/dan35885},
NOTE = {An English translation was published
in \textit{Sov. Math., Dokl.} \textbf{12}
(1971). MR:272855.},
ISSN = {0002-3264},
}
V. V. Kuznetsov and A. S. Shvarts :
“Functors in the category of vector spaces ,”
Soviet Mathematics. Doklady
12
(1971 ),
pp. 41–45 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 196 :1 (1971) .
Zbl
0249.18012
article
People
BibTeX
Vladimir Vasilyevich Kuznetsov
Related
@article {key0249.18012z,
AUTHOR = {Kuznetsov, V. V. and Shvarts, A. S.},
TITLE = {Functors in the category of vector spaces},
JOURNAL = {Soviet Mathematics. Doklady},
FJOURNAL = {Sov. Math., Dokl.},
VOLUME = {12},
YEAR = {1971},
PAGES = {41--45},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{196}:1 (1971). Zbl:0249.18012.},
ISSN = {0197-6788},
}
V. N. Likhachev, Yu. S. Tyupkin, and A. S. Shvarts :
“Adiabatic theorem in quantum field theory ,”
Theoret. and Math. Phys.
10 : 1
(January 1972 ),
pp. 42–55 .
English translation of Russian original published in Teor. Mat. Fiz. 10 :1 (1972) .
article
Abstract
People
BibTeX
@article {key47595620,
AUTHOR = {Likhachev, V. N. and Tyupkin, Yu. S.
and Shvarts, A. S.},
TITLE = {Adiabatic theorem in quantum field theory},
JOURNAL = {Theoret. and Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {10},
NUMBER = {1},
MONTH = {January},
YEAR = {1972},
PAGES = {42--55},
DOI = {10.1007/BF01035766},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{10}:1 (1972).},
ISSN = {0040-5779},
}
V. N. Likhachev, Yu. S. Tyupkin, and A. S. Shvarts :
“Adiabaticheskaq teorema v kvantovoy teorii polq ”
[Adiabatic theorem in quantum field theory ],
Teor. Mat. Fiz.
10 : 1
(1972 ),
pp. 63–84 .
An English translation was published in Theoret. and Math. Phys. 10 :1 (1972) .
MR
475468
article
Abstract
People
BibTeX
The paper indicates the definition of a renormalized \( S \) matrix in quantum field theory, based on the passage to the limit from an adiabatic \( S \) matrix in a finite volume, and shows that under certain conditions it is equivalent to the usual definition.
@article {key475468m,
AUTHOR = {Likhachev, V. N. and Tyupkin, Yu. S.
and Shvarts, A. S.},
TITLE = {Adiabaticheskaq teorema v kvantovoy
teorii polq [Adiabatic theorem in quantum
field theory]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {10},
NUMBER = {1},
YEAR = {1972},
PAGES = {63--84},
URL = {http://mi.mathnet.ru/tmf2641},
NOTE = {An English translation was published
in \textit{Theoret. and Math. Phys.}
\textbf{10}:1 (1972). MR:475468.},
ISSN = {0564-6162},
}
Yu. S. Tyupkin and A. Shvarts :
“On the adiabatic change of a stationary state ,”
Theoret. and Math. Phys.
10 : 2
(February 1972 ),
pp. 172–175 .
English translation of Russian original published in Teor. Mat. Fiz. 10 :2 (1972) .
article
Abstract
People
BibTeX
@article {key90977243,
AUTHOR = {Tyupkin, Yu. S. and Shvarts, A},
TITLE = {On the adiabatic change of a stationary
state},
JOURNAL = {Theoret. and Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {10},
NUMBER = {2},
MONTH = {February},
YEAR = {1972},
PAGES = {172--175},
DOI = {10.1007/BF01090729},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{10}:2 (1972).},
ISSN = {0040-5779},
}
Yu. S. Tyupkin and A. Shvarts :
“Ob adiabaticheskom izmenenii stacionarnogo sostoqniq ”
[On the adiabatic change of a stationary state ],
Teor. Mat. Fiz.
10 : 2
(1972 ),
pp. 259–263 .
An English translation was published in Theoret. and Math. Phys. 10 :2 (1972) .
article
People
BibTeX
@article {key71946953,
AUTHOR = {Tyupkin, Yu. S. and Shvarts, A},
TITLE = {Ob adiabaticheskom izmenenii stacionarnogo
sostoqniq [On the adiabatic change of
a stationary state]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {10},
NUMBER = {2},
YEAR = {1972},
PAGES = {259--263},
URL = {http://mi.mathnet.ru/tmf2719},
NOTE = {An English translation was published
in \textit{Theoret. and Math. Phys.}
\textbf{10}:2 (1972).},
ISSN = {0564-6162},
}
V. A. Fateev and A. S. Švarc :
“Odevaüwie operatorj v kvantovoy teorii polq ”
[Dressing operators in quantum field theory ],
Dokl. Akad. Nauk SSSR
209 : 1
(1973 ),
pp. 66–69 .
An English translation was published in Soviet Physics. Doklady 18 (1973) .
MR
426693
article
People
BibTeX
Vladimir Aleksandrovich Fateev
Related
@article {key426693m,
AUTHOR = {Fateev, V. A. and \v{S}varc, A. S.},
TITLE = {Odeva\"uwie operatorj v kvantovoy teorii
polq [Dressing operators in quantum
field theory]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {209},
NUMBER = {1},
YEAR = {1973},
PAGES = {66--69},
URL = {http://mi.mathnet.ru/eng/dan37505},
NOTE = {An English translation was published
in \textit{Soviet Physics. Doklady}
\textbf{18} (1973). MR:426693.},
ISSN = {0002-3264},
}
V. A. Fateev and A. S. Schwarz :
“K aksiomaticheskoy teorii rasseqniq ”
[On axiomatic scattering theory ],
Teor. Mat. Fiz.
14 : 2
(1973 ),
pp. 152–169 .
An English translation was published in Theoret. and Math. Phys. 14 :2 (1973) .
article
People
BibTeX
Vladimir Aleksandrovich Fateev
Related
@article {key68526487,
AUTHOR = {Fateev, V. A. and Schwarz, A. S.},
TITLE = {K aksiomaticheskoy teorii rasseqniq
[On axiomatic scattering theory]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {14},
NUMBER = {2},
YEAR = {1973},
PAGES = {152--169},
URL = {http://mi.mathnet.ru/tmf3374},
NOTE = {An English translation was published
in \textit{Theoret. and Math. Phys.}
\textbf{14}:2 (1973).},
ISSN = {0564-6162},
}
V. A. Fateev and A. S. Shvarts :
“On axiomatic scattering theory ,”
Theoret. and Math. Phys.
14 : 2
(February 1973 ),
pp. 112–124 .
English translation of Russian original published in Teor. Mat. Fiz. 14 :2 (1973) .
Zbl
0274.47006
article
Abstract
People
BibTeX
Vladimir Aleksandrovich Fateev
Related
@article {key0274.47006z,
AUTHOR = {Fateev, V. A. and Shvarts, A. S.},
TITLE = {On axiomatic scattering theory},
JOURNAL = {Theoret. and Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {14},
NUMBER = {2},
MONTH = {February},
YEAR = {1973},
PAGES = {112--124},
DOI = {10.1007/BF01036349},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{14}:2 (1973). Zbl:0274.47006.},
ISSN = {0040-5779},
}
V. A. Fateev and A. S. Švarc :
“Dressing operators in quantum field theory ,”
Sov. Phys., Dokl.
18
(1973 ),
pp. 165–167 .
English translation of Russian original published in Dokl. Akad. Nauk SSSR 209 :1 (1973) .
Zbl
0288.47009
article
People
BibTeX
Vladimir Aleksandrovich Fateev
Related
@article {key0288.47009z,
AUTHOR = {Fateev, V. A. and \v{S}varc, A. S.},
TITLE = {Dressing operators in quantum field
theory},
JOURNAL = {Sov. Phys., Dokl.},
FJOURNAL = {Soviet Physics. Doklady},
VOLUME = {18},
YEAR = {1973},
PAGES = {165--167},
NOTE = {English translation of Russian original
published in \textit{Dokl. Akad. Nauk
SSSR} \textbf{209}:1 (1973). Zbl:0288.47009.},
ISSN = {0038-5689},
}
A. S. Schwarz :
“Adiabatic theorem in axiomatic quantum field theory ,”
Comm. Math. Phys.
39 : 1
(March 1974 ),
pp. 33–48 .
MR
363291
article
Abstract
BibTeX
It is shown that Møller matrices \( S_{\pm} \) and scattering matrix \( S \) in axiomatic field theory can be expressed through their adiabatic analogs. In particular, it is proved under certain conditions that
\[ S_{-} = \operatorname{slim}\limits_{\alpha\to 0} S_{\alpha}(0,-\infty)\,W_{\alpha} \]
where \( W_{\alpha} \) is a trivial phase factor [i.e. a unitary operator of the form
\[ \exp \frac{i}{\alpha} \int r(\mathbf{k})\,a^+(\mathbf{k})\,a(\mathbf{k})\,d\mathbf{k} \,]. \]
Corresponding results in Hamiltonian approach are discussed.
@article {key363291m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Adiabatic theorem in axiomatic quantum
field theory},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {39},
NUMBER = {1},
MONTH = {March},
YEAR = {1974},
PAGES = {33--48},
DOI = {10.1007/BF01609169},
NOTE = {MR:363291.},
ISSN = {0010-3616},
}
Yu. S. Tyupkin, V. A. Fateev, and A. S. Shvarts :
“Connection between particle-like solutions of classical equations and quantum particles ,”
Soviet J. Nuclear Phys.
22 : 3
(1975 ),
pp. 321–325 .
English translation of Russian original published in Jadernaja Fiz. 22 :3 (1975) .
MR
406170
article
People
BibTeX
@article {key406170m,
AUTHOR = {Tyupkin, Yu. S. and Fateev, V. A. and
Shvarts, A. S.},
TITLE = {Connection between particle-like solutions
of classical equations and quantum particles},
JOURNAL = {Soviet J. Nuclear Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {22},
NUMBER = {3},
YEAR = {1975},
PAGES = {321--325},
NOTE = {English translation of Russian original
published in \textit{Jadernaja Fiz.}
\textbf{22}:3 (1975). MR:406170.},
ISSN = {0038-5506},
}
A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Yu. S. Tyupkin :
“Pseudoparticle solutions of the Yang–Mills equations ,”
Phys. Lett. B
59 : 1
(1975 ),
pp. 85–87 .
MR
434183
article
Abstract
People
BibTeX
@article {key434183m,
AUTHOR = {Belavin, A. A. and Polyakov, A. M. and
Schwartz, A. S. and Tyupkin, Yu. S.},
TITLE = {Pseudoparticle solutions of the {Y}ang--{M}ills
equations},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters B},
VOLUME = {59},
NUMBER = {1},
YEAR = {1975},
PAGES = {85--87},
DOI = {10.1016/0370-2693(75)90163-X},
NOTE = {MR:434183.},
ISSN = {0370-2693},
}
J. S. Tjupkin, V. A. Fateev, and A. S. Švarc :
“O klassicheskom predele matricj rasseqniq v kvantovoy teorii polq ”
[The classical limit of the scattering matrix in quantum field theory ],
Dokl. Akad. Nauk SSSR
221 : 1
(1975 ),
pp. 70–73 .
MR
378641
article
Abstract
People
BibTeX
The present paper investigates the relationships between the particle-like solutions of classical nonlinear translationally invariant equations and the particles in quantum field theory. Scattering in the quantum and classical cases is also compared. The relationships are traced, in particular, for an exactly solvable model, a nonlinear, one-dimensional Schrödinger equation.
@article {key378641m,
AUTHOR = {Tjupkin, Ju. S. and Fateev, V. A. and
\v{S}varc, A. S.},
TITLE = {O klassicheskom predele matricj rasseqniq
v kvantovoy teorii polq [The classical
limit of the scattering matrix in quantum
field theory]},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {221},
NUMBER = {1},
YEAR = {1975},
PAGES = {70--73},
DOI = {http://mi.mathnet.ru/dan38890},
NOTE = {MR:378641.},
ISSN = {0002-3264},
}
A. S. Shvarts :
Matematicheskie osnovj kvantovoy teorii polq
[The mathematical foundations of quantum field theory ].
Atomizdat (Moscow ),
1975 .
An English-language book with equivalent title published by the author in 2020 , presumably based on this.
MR
468857
book
BibTeX
@book {key468857m,
AUTHOR = {Shvarts, A. S.},
TITLE = {Matematicheskie osnovj kvantovoy teorii
polq [The mathematical foundations of
quantum field theory]},
PUBLISHER = {Atomizdat},
ADDRESS = {Moscow},
YEAR = {1975},
PAGES = {368},
NOTE = {An English-language book with equivalent
title published by the author in 2020,
presumably based on this. MR:468857.},
}
A. S. Švarc :
“Suwestvovanie solitonov i obobwennjx solitonov u odnomernjx nelineynjx uravneniy ”
[The existence of solitons and generalized solitons in one-dimensional nonlinear equations ],
Teor. Mat. Fiz.
24 : 3
(1975 ),
pp. 333–346 .
An English translation was published in Theoret. and Math. Phys. 24 :3 (1975) .
MR
487096
article
BibTeX
@article {key487096m,
AUTHOR = {\v{S}varc, A. S.},
TITLE = {Suwestvovanie solitonov i obobwennjx
solitonov u odnomernjx nelineynjx uravneniy
[The existence of solitons and generalized
solitons in one-dimensional nonlinear
equations]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {24},
NUMBER = {3},
YEAR = {1975},
PAGES = {333--346},
URL = {http://mi.mathnet.ru/tmf4018},
NOTE = {An English translation was published
in \textit{Theoret. and Math. Phys.}
\textbf{24}:3 (1975). MR:487096.},
ISSN = {0564-6162},
}
A. S. Shvarts :
Élementj kvantovoy teorii polq: Bozonnje vzaimodey stviq
[Elements of quantum field theory: Boson interactions ].
Atomizdat (Moscow ),
1975 .
MR
489505
book
BibTeX
@book {key489505m,
AUTHOR = {Shvarts, A. S.},
TITLE = {\'Elementj kvantovoy teorii polq: {B}ozonnje
vzaimodey stviq [Elements of quantum
field theory: {B}oson interactions]},
PUBLISHER = {Atomizdat},
ADDRESS = {Moscow},
YEAR = {1975},
PAGES = {192},
NOTE = {MR:489505.},
}
A. S. Shvarts :
“Existence of solitons and generalized solitons for one-dimensional nonlinear equations ,”
Theoret. and Math. Phys.
24 : 3
(September 1975 ),
pp. 868–878 .
English translation of Russian original published in Teor. Mat. Fiz. 24 :3 (1975) .
article
Abstract
BibTeX
@article {key72449315,
AUTHOR = {Shvarts, A. S.},
TITLE = {Existence of solitons and generalized
solitons for one-dimensional nonlinear
equations},
JOURNAL = {Theoret. and Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {24},
NUMBER = {3},
MONTH = {September},
YEAR = {1975},
PAGES = {868--878},
DOI = {10.1007/BF01029873},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{24}:3 (1975).},
ISSN = {0040-5779},
}
Yu. S. Tyupkin, V. A. Fateev, and A. S. Shvarts :
“Connection between particle-like solutions of classical equations and quantum particles ,”
Jadernaja Fiz.
22 : 3
(1975 ),
pp. 622–631 .
An English translation was published in Soviet J. Nuclear Phys. 22 :3 (1975) .
article
People
BibTeX
@article {key81063248,
AUTHOR = {Tyupkin, Yu. S. and Fateev, V. A. and
Shvarts, A. S.},
TITLE = {Connection between particle-like solutions
of classical equations and quantum particles},
JOURNAL = {Jadernaja Fiz.},
FJOURNAL = {Jadernaja Fizika},
VOLUME = {22},
NUMBER = {3},
YEAR = {1975},
PAGES = {622--631},
NOTE = {An English translation was published
in \textit{Soviet J. Nuclear Phys.}
\textbf{22}:3 (1975).},
ISSN = {0044-0027},
}
A. Schwarz, V. Fateev, and Yu. Tyupkin :
Topologically non-trivial particles in quantum field theory .
Technical report 157 ,
Lebedev Institute ,
1975 .
In Russian.
techreport
People
BibTeX
@techreport {key33351224,
AUTHOR = {Schwarz, A. and V. Fateev and Yu. Tyupkin},
TITLE = {Topologically non-trivial particles
in quantum field theory},
TYPE = {technical report},
NUMBER = {157},
INSTITUTION = {Lebedev Institute},
YEAR = {1975},
NOTE = {In Russian.},
}
A. S. Schwarz, Yu. Tyupkin, and V. Fateev :
“On topologically non-trivial particles in quantum field theory ,”
Pisma Zh. Èksper. Teoret. Fiz.
22
(1975 ),
pp. 192–194 .
In Russian; translated into English in JETP Letters 22 :3 (1975), 88–89.
article
People
BibTeX
@article {key14138055,
AUTHOR = {Schwarz, A. S. and Yu. Tyupkin and V.
Fateev},
TITLE = {On topologically non-trivial particles
in quantum field theory},
JOURNAL = {Pisma Zh. \`Eksper. Teoret. Fiz.},
VOLUME = {22},
YEAR = {1975},
PAGES = {192--194},
URL = {http://jetpletters.ru/ps/1522/article_23294.pdf},
NOTE = {In Russian; translated into English
in \textit{JETP Letters} \textbf{22}:3
(1975), 88--89.},
}
A. S. Schwarz, Yu. Tyupkin, and V. Fateev :
“On the existence of heavy particles in gauge fields theories ,”
Pisma Zh. Èksper. Teoret. Fiz.
21
(1975 ),
pp. 91–93 .
In Russian.
article
People
BibTeX
@article {key54429510,
AUTHOR = {Schwarz, A. S. and Yu. Tyupkin and V.
Fateev},
TITLE = {On the existence of heavy particles
in gauge fields theories},
JOURNAL = {Pisma Zh. \`Eksper. Teoret. Fiz.},
VOLUME = {21},
YEAR = {1975},
PAGES = {91--93},
NOTE = {In Russian.},
}
J. S. Tjupkin, V. A. Fateev, and A. S. Švarc :
“CHasticepodobnje resheniq uravneniy kalibrovochnjx teoriy polq ”
[Particle-like solutions of the equations of gauge theories ],
Teor. Mat. Fiz.
26 : 3
(1976 ),
pp. 397–402 .
An English translation was published in Theoret. and Math. Phys. 26 :3 (1976) .
MR
449236
article
People
BibTeX
@article {key449236m,
AUTHOR = {Tjupkin, Ju. S. and Fateev, V. A. and
\v{S}varc, A. S.},
TITLE = {CHasticepodobnje resheniq uravneniy
kalibrovochnjx teoriy polq [Particle-like
solutions of the equations of gauge
theories]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {26},
NUMBER = {3},
YEAR = {1976},
PAGES = {397--402},
URL = {http://mi.mathnet.ru/tmf3239},
NOTE = {An English translation was published
in \textit{Theoret. and Math. Phys.}
\textbf{26}:3 (1976). MR:449236.},
ISSN = {0564-6162},
}
A. S. Schwarz :
“Magnetic monopoles in gauge theories ,”
Nuclear Phys. B
112 : 2
(September 1976 ),
pp. 358–364 .
MR
416313
article
Abstract
BibTeX
@article {key416313m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Magnetic monopoles in gauge theories},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physiscs B},
VOLUME = {112},
NUMBER = {2},
MONTH = {September},
YEAR = {1976},
PAGES = {358--364},
DOI = {10.1016/0550-3213(76)90538-1},
NOTE = {MR:416313.},
ISSN = {0550-3213},
}
A. S. Schwarz :
“Topologically nontrivial solitons of classical equations and their role in quantum field theory ,”
pp. 224–240
in
Nonlocal, nonlinear and nonrenormalizable field theories: Proceedings of the 4th international symposium on nonlocal field theories
(Alushta, USSR, 20–28 April 1976 ).
Edited by D. I. Blokhintsev .
Joint Institute For Nuclear Research (Dubna, USSR ),
1976 .
MR
0456147
incollection
People
BibTeX
@incollection {key78041945,
AUTHOR = {Schwarz, A. S.},
TITLE = {Topologically nontrivial solitons of
classical equations and their role in
quantum field theory},
BOOKTITLE = {Nonlocal, nonlinear and nonrenormalizable
field theories: {P}roceedings of the
4th international symposium on nonlocal
field theories},
EDITOR = {Blokhintsev, D. I.},
PUBLISHER = {Joint Institute For Nuclear Research},
ADDRESS = {Dubna, USSR},
YEAR = {1976},
PAGES = {224--240},
NOTE = {(Alushta, USSR, 20--28 April 1976).},
}
Yu. S. Tyupkin, V. A. Fateev, and A. S. Shvarts :
“Particle-like solutions of the equations of gauge theories ,”
Theoret. and Math. Phys.
26 : 3
(March 1976 ),
pp. 270–273 .
English translation of Russian origianl published in Teor. Mat. Fiz. 26 :3 (1976) .
article
Abstract
People
BibTeX
@article {key70058705,
AUTHOR = {Tyupkin, Yu. S. and Fateev, V. A. and
Shvarts, A. S.},
TITLE = {Particle-like solutions of the equations
of gauge theories},
JOURNAL = {Theoret. and Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {26},
NUMBER = {3},
MONTH = {March},
YEAR = {1976},
PAGES = {270--273},
DOI = {10.1007/BF01032100},
NOTE = {English translation of Russian origianl
published in \textit{Teor. Mat. Fiz.}
\textbf{26}:3 (1976).},
ISSN = {0040-5779},
}
A. Schwarz, V. Fateev, and Yu. Tyupkin :
On the particle-like solutions in the presence of fermions .
Technical report 155 ,
Lebedev Institute ,
1976 .
In Russian.
techreport
People
BibTeX
@techreport {key86364857,
AUTHOR = {Schwarz, A. and V. Fateev and Yu. Tyupkin},
TITLE = {On the particle-like solutions in the
presence of fermions},
TYPE = {technical report},
NUMBER = {155},
INSTITUTION = {Lebedev Institute},
YEAR = {1976},
NOTE = {In Russian.},
}
A. S. Schwarz :
“Magnetic monopoles in gauge field theories ,”
Uspekhi Matematicheskikh Nauk (Russian Mathematical Surveys)
31 : 3
(1976 ),
pp. 248–258 .
In Russian.
article
BibTeX
@article {key95864323,
AUTHOR = {Schwarz, A. S.},
TITLE = {Magnetic monopoles in gauge field theories},
JOURNAL = {Uspekhi Matematicheskikh Nauk (Russian
Mathematical Surveys)},
VOLUME = {31},
NUMBER = {3},
YEAR = {1976},
PAGES = {248--258},
URL = {http://www.mathnet.ru/links/22cc0bbeaf443898ddad6b5998ac41dd/rm3749.pdf},
NOTE = {In Russian.},
}
A. S. Schwarz :
“Topologically nontrivial solutions of classical equations and
their role in quantum field theory ,”
pp. 224–240
in
Nonlocal, nonlinear and nonrenormalizable field theories (Proc. Fourth Internat. Sympos. Nonlocal Field Theories)
(Alushta, 1976 ).
Edited by D. I. Blokhintsev .
1976 .
In Russian.
MR
456147
inproceedings
People
BibTeX
@inproceedings {key456147m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Topologically nontrivial solutions of
classical equations and their role in
quantum field theory},
BOOKTITLE = {Nonlocal, nonlinear and nonrenormalizable
field theories ({P}roc. {F}ourth {I}nternat.
{S}ympos. {N}onlocal {F}ield {T}heories)},
EDITOR = {Blokhintsev, D. I.},
YEAR = {1976},
PAGES = {224--240},
NOTE = {({A}lushta, 1976). In {R}ussian. MR:456147.},
}
A. S. Schwarz :
“On regular solutions of Euclidean Yang–Mills equations ,”
Phys. Lett. B
67 : 2
(1977 ),
pp. 172–174 .
MR
443673
article
Abstract
BibTeX
@article {key443673m,
AUTHOR = {Schwarz, A. S.},
TITLE = {On regular solutions of {E}uclidean
{Y}ang--{M}ills equations},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters. B. Particle Physics,
Nuclear Physics and Cosmology},
VOLUME = {67},
NUMBER = {2},
YEAR = {1977},
PAGES = {172--174},
DOI = {10.1016/0370-2693(77)90095-8},
NOTE = {MR:443673.},
ISSN = {0370-2693},
}
A. S. Schwarz :
“On symmetric gauge fields ,”
Comm. Math. Phys.
56 : 1
(1977 ),
pp. 79–86 .
MR
457641
Zbl
0361.53030
article
Abstract
BibTeX
@article {key457641m,
AUTHOR = {Schwarz, A. S.},
TITLE = {On symmetric gauge fields},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {56},
NUMBER = {1},
YEAR = {1977},
PAGES = {79--86},
DOI = {10.1007/BF01611118},
URL = {http://projecteuclid.org/euclid.cmp/1103901086},
NOTE = {MR:457641. Zbl:0361.53030.},
ISSN = {0010-3616},
}
V. N. Romanov, A. S. Schwarz, and Yu. S. Tyupkin :
“On spherically symmetric fields in gauge theories ,”
Nuclear Phys. B
130 : 2
(1977 ),
pp. 209–220 .
MR
496156
article
Abstract
People
BibTeX
@article {key496156m,
AUTHOR = {Romanov, V. N. and Schwarz, A. S. and
Tyupkin, Yu. S.},
TITLE = {On spherically symmetric fields in gauge
theories},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {130},
NUMBER = {2},
YEAR = {1977},
PAGES = {209--220},
DOI = {10.1016/0550-3213(77)90104-3},
NOTE = {MR:496156.},
ISSN = {0550-3213},
}
A. S. Schwarz :
“On quantum fluctuations of instantons ,”
Lett. Math. Phys.
2 : 3
(1978 ),
pp. 201–205 .
MR
495474
Zbl
0383.70016
article
Abstract
BibTeX
@article {key495474m,
AUTHOR = {Schwarz, A. S.},
TITLE = {On quantum fluctuations of instantons},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {2},
NUMBER = {3},
YEAR = {1978},
PAGES = {201--205},
DOI = {10.1007/BF00406406},
NOTE = {MR:495474. Zbl:0383.70016.},
ISSN = {0377-9017},
}
V. N. Romanov, I. V. Frolov, and A. S. Švarc :
“O sfericheski-simmetrichnjx solitonax ”
[Spherically symmetric solitons ],
Teor. Mat. Fiz.
37 : 3
(1978 ),
pp. 305–318 .
An English translation was published in Theor. Math. Phys. 37 :3 (1978) .
MR
524695
article
People
BibTeX
@article {key524695m,
AUTHOR = {Romanov, V. N. and Frolov, I. V. and
\v{S}varc, A. S.},
TITLE = {O sfericheski-simmetrichnjx solitonax
[Spherically symmetric solitons]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {37},
NUMBER = {3},
YEAR = {1978},
PAGES = {305--318},
URL = {http://mi.mathnet.ru/eng/tmf3121},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{37}:3
(1978). MR:524695.},
ISSN = {0564-6162},
}
A. S. Schwarz :
“The partition function of degenerate quadratic functional and Ray–Singer invariants ,”
Lett. Math. Phys.
2 : 3
(1978 ),
pp. 247–252 .
MR
676337
Zbl
0383.70017
article
Abstract
BibTeX
@article {key676337m,
AUTHOR = {Schwarz, A. S.},
TITLE = {The partition function of degenerate
quadratic functional and {R}ay--{S}inger
invariants},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {2},
NUMBER = {3},
YEAR = {1978},
PAGES = {247--252},
DOI = {10.1007/BF00406412},
NOTE = {MR:676337. Zbl:0383.70017.},
ISSN = {0377-9017},
}
V. N. Romanov, I. V. Frolov, and A. S. Schwarz :
“Spherically symmetric solitons ,”
Theor. Math. Phys.
37 : 3
(1978 ),
pp. 1038–1046 .
English translation of Russian original published in Teor. Mat. Fiz. 37 :3 (1978) .
article
Abstract
People
BibTeX
@article {key96908161,
AUTHOR = {Romanov, V. N. and Frolov, I. V. and
Schwarz, A. S.},
TITLE = {Spherically symmetric solitons},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {37},
NUMBER = {3},
YEAR = {1978},
PAGES = {1038--1046},
DOI = {10.1007/BF01018584},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{37}:3 (1978).},
ISSN = {0040-5779},
}
A. S. Schwarz and I. Frolov :
“Contribution of instantons to the correlation functions of a Heisenberg ferromagnet ,”
Pisma Zh. Èksper. Teoret. Fiz.
28
(1978 ),
pp. 274–276 .
In Russian; translated in JETP Letters 28 , p. 249.
article
People
BibTeX
@article {key41414339,
AUTHOR = {Schwarz, A. S. and Frolov, I.},
TITLE = {Contribution of instantons to the correlation
functions of a Heisenberg ferromagnet},
JOURNAL = {Pisma Zh. \`Eksper. Teoret. Fiz.},
VOLUME = {28},
YEAR = {1978},
PAGES = {274--276},
NOTE = {In Russian; translated in \textit{JETP
Letters} \textbf{28}, p. 249.},
}
V. A. Fateev, I. V. Frolov, and A. S. Shvarts :
“Kvantovye fluktuatsii instantonov v dvumernykh nelinejnykh teoriyakh ”
[Quantum fluctuations of instantons in two-dimensional nonlinear theories ],
Yadernaya Fiz.
30 : 4
(1979 ),
pp. 1134–1147 .
An English translation was published in Sov. J. Nucl. Phys. 30 :4 (1979) .
MR
576531
article
People
BibTeX
@article {key576531m,
AUTHOR = {Fateev, V. A. and Frolov, I. V. and
Shvarts, A. S.},
TITLE = {Kvantovye fluktuatsii instantonov v
dvumernykh nelinejnykh teoriyakh [Quantum
fluctuations of instantons in two-dimensional
nonlinear theories]},
JOURNAL = {Yadernaya Fiz.},
FJOURNAL = {Yadernaya Fizika. Akademiya Nauk SSSR},
VOLUME = {30},
NUMBER = {4},
YEAR = {1979},
PAGES = {1134--1147},
NOTE = {An English translation was published
in \textit{Sov. J. Nucl. Phys.} \textbf{30}:4
(1979). MR:576531.},
ISSN = {0044-0027},
}
A. A. Belavin, V. A. Fateev, A. S. Schwarz, and Yu. S. Tyupkin :
“Quantum fluctuations of multi-instanton solutions ,”
Nuclear Phys. B
83 : 3–4
(May 1979 ),
pp. 317–320 .
article
Abstract
People
BibTeX
@article {key70508533,
AUTHOR = {Belavin, A. A. and Fateev, V. A. and
Schwarz, A. S. and Tyupkin, Yu. S.},
TITLE = {Quantum fluctuations of multi-instanton
solutions},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physiscs B},
VOLUME = {83},
NUMBER = {3--4},
MONTH = {May},
YEAR = {1979},
PAGES = {317--320},
DOI = {10.1016/0370-2693(79)91117-1},
ISSN = {0550-3213},
}
V. A. Fateev, I. V. Frolov, and A. S. Shvarts :
“Quantum fluctuations of instantons in two-dimensional nonlinear theories ,”
Sov. J. Nucl. Phys.
30 : 4
(1979 ).
English translation of Russian original published in Yadernaya Fiz. 30 :4 (1979) .
article
Abstract
People
BibTeX
@article {key59046371,
AUTHOR = {Fateev, V. A. and Frolov, I. V. and
Shvarts, A. S.},
TITLE = {Quantum fluctuations of instantons in
two-dimensional nonlinear theories},
JOURNAL = {Sov. J. Nucl. Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {30},
NUMBER = {4},
YEAR = {1979},
NOTE = {English translation of Russian original
published in \textit{Yadernaya Fiz.}
\textbf{30}:4 (1979).},
ISSN = {0044-0027},
}
V. A. Fateev, I. V. Frolov, and A. S. Schwarz :
“Quantum fluctuations of instantons in the nonlinear \( \sigma \) model ,”
Nuclear Phys. B
154 : 1
(July 1979 ),
pp. 1–20 .
article
Abstract
People
BibTeX
@article {key98017983,
AUTHOR = {Fateev, V. A. and Frolov, I. V. and
Schwarz, A. S.},
TITLE = {Quantum fluctuations of instantons in
the nonlinear \$\sigma\$ model},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physiscs B},
VOLUME = {154},
NUMBER = {1},
MONTH = {July},
YEAR = {1979},
PAGES = {1--20},
DOI = {10.1016/0550-3213(79)90367-5},
ISSN = {0550-3213},
}
I. V. Frolov and A. S. Schwarz :
“On the instanton contribution in euclidean green functions ,”
Phys. Lett. B
80 : 4–5
(1979 ),
pp. 406–409 .
article
Abstract
People
BibTeX
@article {key38581373,
AUTHOR = {Frolov, I. V. and Schwarz, A. S.},
TITLE = {On the instanton contribution in euclidean
green functions},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters. B. Particle Physics,
Nuclear Physics and Cosmology},
VOLUME = {80},
NUMBER = {4--5},
YEAR = {1979},
PAGES = {406--409},
DOI = {10.1016/0370-2693(79)91201-2},
ISSN = {0370-2693},
}
A. S. Schwarz :
“Instantons and fermions in the field of instanton ,”
Comm. Math. Phys.
64 : 3
(1979 ),
pp. 233–268 .
MR
520092
Zbl
0406.58032
article
Abstract
BibTeX
@article {key520092m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Instantons and fermions in the field
of instanton},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {64},
NUMBER = {3},
YEAR = {1979},
PAGES = {233--268},
DOI = {10.1007/BF01221733},
URL = {http://projecteuclid.org/euclid.cmp/1103904722},
NOTE = {MR:520092. Zbl:0406.58032.},
ISSN = {0010-3616},
}
A. S. Schwarz :
“The partition function of a degenerate functional ,”
Comm. Math. Phys.
67 : 1
(1979 ),
pp. 1–16 .
MR
535228
Zbl
0429.58015
article
Abstract
BibTeX
@article {key535228m,
AUTHOR = {Schwarz, A. S.},
TITLE = {The partition function of a degenerate
functional},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {67},
NUMBER = {1},
YEAR = {1979},
PAGES = {1--16},
DOI = {10.1007/BF01223197},
URL = {http://projecteuclid.org/euclid.cmp/1103905113},
NOTE = {MR:535228. Zbl:0429.58015.},
ISSN = {0010-3616},
}
V. N. Romanov and A. S. Švarc :
“Anomalii i ällipticheskie operatorj ”
[Anomalies and elliptic operators ],
Teor. Mat. Fiz.
41 : 2
(1979 ),
pp. 190–204 .
An English translation was published in Theor. Math. Phys. 41 :2 (1979) .
MR
555848
article
People
BibTeX
@article {key555848m,
AUTHOR = {Romanov, V. N. and \v{S}varc, A. S.},
TITLE = {Anomalii i \"allipticheskie operatorj
[Anomalies and elliptic operators]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {41},
NUMBER = {2},
YEAR = {1979},
PAGES = {190--204},
URL = {http://mi.mathnet.ru/tmf3054},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{41}:2
(1979). MR:555848.},
ISSN = {0564-6162},
}
V. N. Romanov and A. S. Schwarz :
“Anomalies and elliptic operators ,”
Theor. Math. Phys.
41 : 2
(November 1979 ),
pp. 967–977 .
English translation of Russian original published in Teor. Mat. Fiz. 41 :2 (1979) .
article
Abstract
People
BibTeX
The coefficients of the asymptotic expansion of \( \operatorname{Sp}\exp(-tA) \) in the limit \( t\to 0 \) for the operators of quantum field theory are calculated and it is shown how the obtained results can be applied to the calculation of the axial and conformal anomalies, charge renormalization in gauge theories, and to the investigation of two-dimensional electrodynamics.
@article {key86169708,
AUTHOR = {Romanov, V. N. and Schwarz, A. S.},
TITLE = {Anomalies and elliptic operators},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {41},
NUMBER = {2},
MONTH = {November},
YEAR = {1979},
PAGES = {967--977},
DOI = {10.1007/BF01028502},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{41}:2 (1979).},
ISSN = {0040-5779},
}
A. S. Schwarz, A. Belavin, V. Fateev, and Yu. Tyupkin :
“Quantum fluctuations of multi-instantons solutions ,”
Physics Letters B
83 : 3–4
(1979 ),
pp. 317–320 .
article
BibTeX
@article {key47287453,
AUTHOR = {Schwarz, A. S. and Belavin, A. and Fateev,
V. and Tyupkin, Yu.},
TITLE = {Quantum fluctuations of multi-instantons
solutions},
JOURNAL = {Physics Letters B},
VOLUME = {83},
NUMBER = {3--4},
YEAR = {1979},
PAGES = {317--320},
DOI = {10.1016/0370-2693(79)91117-1},
}
A. S. Schwarz, V. Fateev, and I. Frolov :
“Quantum fluctuations of instantons in the non-linear \( \sigma \) -model ,”
Nuclear Physics B
154
(1979 ),
pp. 1–20 .
article
People
BibTeX
@article {key21847958,
AUTHOR = {Schwarz, A. S. and Fateev, V. and Frolov,
I.},
TITLE = {Quantum fluctuations of instantons in
the non-linear \$\sigma\$-model},
JOURNAL = {Nuclear Physics B},
VOLUME = {154},
YEAR = {1979},
PAGES = {1--20},
DOI = {10.1016/0550-3213(79)90367-5},
}
A. S. Schwarz and I. Frolov :
“On the instanton contribution in Euclidean Green functions ,”
Physics Letters B
80 : 4–5
(1979 ),
pp. 406–409 .
article
BibTeX
@article {key72522525,
AUTHOR = {A. S. Schwarz and I. Frolov},
TITLE = {On the instanton contribution in Euclidean
Green functions},
JOURNAL = {Physics Letters B},
VOLUME = {80},
NUMBER = {4--5},
YEAR = {1979},
PAGES = {406--409},
DOI = {10.1016/0370-2693(79)91201-2},
}
V. A. Fateev, I. V. Frolov, and A. S. Schwarz :
“Quantum fluctuations of instantons in a two-dimensional nonlinear anisotropic sigma-model ,”
Yadernaya Fiz.
32 : 1
(1980 ),
pp. 299–300 .
An English translation was published in Sov. J. Nucl. Phys. 32 :1 (1980) .
MR
618462
article
People
BibTeX
@article {key618462m,
AUTHOR = {Fateev, V. A. and Frolov, I. V. and
Schwarz, A. S.},
TITLE = {Quantum fluctuations of instantons in
a two-dimensional nonlinear anisotropic
sigma-model},
JOURNAL = {Yadernaya Fiz.},
FJOURNAL = {Yadernaya Fizika. Akademiya Nauk SSSR},
VOLUME = {32},
NUMBER = {1},
YEAR = {1980},
PAGES = {299--300},
NOTE = {An English translation was published
in \textit{Sov. J. Nucl. Phys.} \textbf{32}:1
(1980). MR:618462.},
ISSN = {0044-0027},
}
V. A. Fateev, I. V. Frolov, and A. S. Schwarz :
“Quantum fluctuations of instantons in a two-dimensional nonlinear anisotropic sigma-model ,”
Sov. J. Nucl. Phys.
32 : 1
(1980 ).
English translation of Russian original published in Yadernaya Fiz. 32 :1 (1980) .
article
Abstract
People
BibTeX
We consider a two-dimensional model describing fields with values on a surface which is topologically equivalent to the two-sphere, but having an arbitrary metric. The contribution of instantons to this model is calculated. This contribution does not differ significantly from that found in the sigma model.
@article {key92822185,
AUTHOR = {Fateev, V. A. and Frolov, I. V. and
Schwarz, A. S.},
TITLE = {Quantum fluctuations of instantons in
a two-dimensional nonlinear anisotropic
sigma-model},
JOURNAL = {Sov. J. Nucl. Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {32},
NUMBER = {1},
YEAR = {1980},
NOTE = {English translation of Russian original
published in \textit{Yadernaya Fiz.}
\textbf{32}:1 (1980).},
ISSN = {0044-0027},
}
O. M. Khudaverdian and A. S. Schwarz :
“A few comments on the string representation of gauge fields ,”
Phys. Lett. B
91 : 1
(March 1980 ),
pp. 107–110 .
article
Abstract
People
BibTeX
@article {key30667094,
AUTHOR = {Khudaverdian, O. M. and Schwarz, A.
S.},
TITLE = {A few comments on the string representation
of gauge fields},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters B},
VOLUME = {91},
NUMBER = {1},
MONTH = {March},
YEAR = {1980},
PAGES = {107--110},
DOI = {10.1016/0370-2693(80)90672-3},
ISSN = {0370-2693},
}
A. S. Schwarz :
“Are the field and space variables on an equal footing? ,”
Nuclear Phys. B
171 : 1–2
(1980 ),
pp. 154–166 .
MR
582926
article
Abstract
BibTeX
@article {key582926m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Are the field and space variables on
an equal footing?},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {171},
NUMBER = {1--2},
YEAR = {1980},
PAGES = {154--166},
DOI = {10.1016/0550-3213(80)90365-X},
NOTE = {MR:582926.},
ISSN = {0550-3213},
}
V. N. Romanov, V. A. Fateev, and A. S. Schwarz :
“Magnitnye monopolii v edinykh teoriyakh ehlektromagnitnogo, slabogo i sil’nogo vzaimodejstviya ”
[Magnetic monopoles in the unified theories of electromagnetic, weak, and strong interactions ],
Yadernaya Fiz.
32 : 4
(1980 ),
pp. 1138–1141 .
An English translation was published in Sov. J. Nucl. Phys. 32 :4 (1980) .
MR
624047
article
People
BibTeX
@article {key624047m,
AUTHOR = {Romanov, V. N. and Fateev, V. A. and
Schwarz, A. S.},
TITLE = {Magnitnye monopolii v edinykh teoriyakh
ehlektromagnitnogo, slabogo i sil'nogo
vzaimodejstviya [Magnetic monopoles
in the unified theories of electromagnetic,
weak, and strong interactions]},
JOURNAL = {Yadernaya Fiz.},
FJOURNAL = {Yadernaya Fizika. Akademiya Nauk SSSR},
VOLUME = {32},
NUMBER = {4},
YEAR = {1980},
PAGES = {1138--1141},
NOTE = {An English translation was published
in \textit{Sov. J. Nucl. Phys.} \textbf{32}:4
(1980). MR:624047.},
ISSN = {0044-0027},
}
V. N. Romanov, V. A. Fateev, and A. S. Schwarz :
“Magnetic monopoles in the unified theories of electromagnetic, weak, and strong interactions ,”
Sov. J. Nucl. Phys.
32 : 4
(1980 ).
English translation of Russian original published in Yadernaya Fiz. 32 :4 (1980) .
article
People
BibTeX
@article {key73350807,
AUTHOR = {Romanov, V. N. and Fateev, V. A. and
Schwarz, A. S.},
TITLE = {Magnetic monopoles in the unified theories
of electromagnetic, weak, and strong
interactions},
JOURNAL = {Sov. J. Nucl. Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {32},
NUMBER = {4},
YEAR = {1980},
NOTE = {English translation of Russian original
published in \textit{Yadernaya Fiz.}
\textbf{32}:4 (1980).},
ISSN = {0044-0027},
}
A. S. Schwarz and Yu. S. Tyupkin :
“Vortices in unified theories of weak and electromagnetic interactions ,”
Phys. Lett. B
90 : 1–2
(February 1980 ),
pp. 135–137 .
article
Abstract
People
BibTeX
@article {key17280430,
AUTHOR = {Schwarz, A. S. and Tyupkin, Yu. S.},
TITLE = {Vortices in unified theories of weak
and electromagnetic interactions},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters B},
VOLUME = {90},
NUMBER = {1--2},
MONTH = {February},
YEAR = {1980},
PAGES = {135--137},
DOI = {10.1016/0370-2693(80)90067-2},
ISSN = {0370-2693},
}
V. A. Fateev, I. V. Frolov, A. S. Schwarz, and Yu. S. Tyupkin :
“Quantum fluctuations of instantons ,”
Sov. Sci. Rev., Sect. C
2
(1981 ),
pp. 1–51 .
MR
659266
Zbl
0535.58026
article
People
BibTeX
@article {key659266m,
AUTHOR = {Fateev, V. A. and Frolov, I. V. and
Schwarz, A. S. and Tyupkin, Yu. S.},
TITLE = {Quantum fluctuations of instantons},
JOURNAL = {Sov. Sci. Rev., Sect. C},
FJOURNAL = {Soviet Scientific Reviews. Section C:
Mathematical Physics Reviews},
VOLUME = {2},
YEAR = {1981},
PAGES = {1--51},
NOTE = {MR:659266. Zbl:0535.58026.},
ISSN = {0143-0416},
}
O. M. Khudaverdyan and A. S. Shvarts :
“Multiplicative functionals and gauge fields ,”
Theor. Math. Phys.
46 : 2
(February 1981 ),
pp. 124–132 .
English translation of Russian original published in Teor. Mat. Fiz. 46 :2 (1981) .
article
Abstract
People
BibTeX
@article {key16115548,
AUTHOR = {Khudaverdyan, O. M. and Shvarts, A.
S.},
TITLE = {Multiplicative functionals and gauge
fields},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {46},
NUMBER = {2},
MONTH = {February},
YEAR = {1981},
PAGES = {124--132},
DOI = {10.1007/BF01030846},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{46}:2 (1981).},
ISSN = {0040-5779},
}
O. M. Hudaverdjan and A. S. Švarc :
“Multiplicative functionals and gauge fields ”
[Mul’tiplikativnje funkcionalj i kalibrovochnje polq ],
Teor. Mat. Fiz.
46 : 2
(1981 ),
pp. 187–198 .
An English translation was published in Theor. Math. Phys. 46 :2 (1981) .
MR
612954
article
People
BibTeX
@article {key612954m,
AUTHOR = {Hudaverdjan, O. M. and \v{S}varc, A.
S.},
TITLE = {Multiplicative functionals and gauge
fields [Mul\cprime tiplikativnje funkcionalj
i kalibrovochnje polq]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {46},
NUMBER = {2},
YEAR = {1981},
PAGES = {187--198},
URL = {http://mi.mathnet.ru/tmf2313},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{46}:2
(1981). MR:612954.},
ISSN = {0564-6162},
}
A. V. Gayduk, V. N. Romanov, and A. S. Schwarz :
“Supergravity and field space democracy ,”
Comm. Math. Phys.
79 : 4
(1981 ),
pp. 507–528 .
MR
623965
article
Abstract
People
BibTeX
If the action functional is determined uniquely by its symmetry properties, we say that this functional is perfect. We study the perfect functionals in the framework in which the space and field variables are on equal footing. This study leads to the natural multidimensional generalizations of supergravity.
@article {key623965m,
AUTHOR = {Gayduk, A. V. and Romanov, V. N. and
Schwarz, A. S.},
TITLE = {Supergravity and field space democracy},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {79},
NUMBER = {4},
YEAR = {1981},
PAGES = {507--528},
DOI = {10.1007/BF01209310},
NOTE = {MR:623965.},
ISSN = {0010-3616},
}
A. S. Schwarz and Yu. S. Tyupkin :
“Dimensional reduction of the gauge field theory ,”
Nuclear Phys. B
187 : 2
(1981 ),
pp. 321–332 .
MR
627104
article
Abstract
People
BibTeX
@article {key627104m,
AUTHOR = {Schwarz, A. S. and Tyupkin, Yu. S.},
TITLE = {Dimensional reduction of the gauge field
theory},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {187},
NUMBER = {2},
YEAR = {1981},
PAGES = {321--332},
DOI = {10.1016/0550-3213(81)90277-7},
NOTE = {MR:627104.},
ISSN = {0550-3213},
}
A. S. Shvarts :
“Jellipticheskie operatorj v kvantovoy teorii polq ”
[Elliptic operators in quantum field theory ],
Sovremennye Problemy Matematiki. Noveishie Dostizheniya
17
(1981 ),
pp. 113–173 .
An English translation was published in J. Soviet Math. 21 :4 (1983) .
MR
628977
Zbl
0482.35080
article
Abstract
BibTeX
@article {key628977m,
AUTHOR = {Shvarts, A. S.},
TITLE = {Jellipticheskie operatorj v kvantovoy
teorii polq [Elliptic operators in quantum
field theory]},
JOURNAL = {Sovremennye Problemy Matematiki. Noveishie
Dostizheniya},
VOLUME = {17},
YEAR = {1981},
PAGES = {113--173},
URL = {http://mi.mathnet.ru/eng/intd49},
NOTE = {An English translation was published
in \textit{J. Soviet Math.} \textbf{21}:4
(1983). MR:628977. Zbl:0482.35080.},
ISSN = {0202-747X},
}
O. M. Khudaverdian, A. S. Schwarz, and Yu. S. Tyupkin :
“Integral invariants for supercanonical transformations ,”
Lett. Math. Phys.
5 : 6
(1981 ),
pp. 517–522 .
MR
637632
Zbl
0521.58054
article
People
BibTeX
@article {key637632m,
AUTHOR = {Khudaverdian, O. M. and Schwarz, A.
S. and Tyupkin, Yu. S.},
TITLE = {Integral invariants for supercanonical
transformations},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {5},
NUMBER = {6},
YEAR = {1981},
PAGES = {517--522},
DOI = {10.1007/BF00408133},
NOTE = {MR:637632. Zbl:0521.58054.},
ISSN = {0377-9017},
}
A. S. Schwarz :
“Supergravity and complex geometry ,”
Yadernaya Fiz.
34 : 4
(1981 ),
pp. 1144–1149 .
An English translation was published in Soviet J. Nuclear Phys. 34 :4 (1981) .
MR
660226
article
BibTeX
@article {key660226m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Supergravity and complex geometry},
JOURNAL = {Yadernaya Fiz.},
FJOURNAL = {Yadernaya Fizika. Akademiya Nauk SSSR},
VOLUME = {34},
NUMBER = {4},
YEAR = {1981},
PAGES = {1144--1149},
NOTE = {An English translation was published
in \textit{Soviet J. Nuclear Phys.}
\textbf{34}:4 (1981). MR:660226.},
ISSN = {0044-0027},
}
A. S. Schwarz :
“Supergravity and complex geometry ,”
Soviet J. Nuclear Phys.
34 : 4
(1981 ),
pp. 635–637 .
English translation of Russian original published in Yadernaya Fiz. 34 :4 (1981) .
article
Abstract
BibTeX
@article {key61927353,
AUTHOR = {Schwarz, A. S.},
TITLE = {Supergravity and complex geometry},
JOURNAL = {Soviet J. Nuclear Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {34},
NUMBER = {4},
YEAR = {1981},
PAGES = {635--637},
NOTE = {English translation of Russian original
published in \textit{Yadernaya Fiz.}
\textbf{34}:4 (1981).},
ISSN = {0038-5506},
}
A. S. Schwarz :
“Theories with nonlocal electric charge conservation ,”
Pisma Zh. Èksper. Teoret. Fiz.
34
(1981 ),
pp. 555–558 .
In Russian; translated in JETP Letters 34 : 10 (1981), 532–534.
article
BibTeX
@article {key38682155,
AUTHOR = {Schwarz, A. S.},
TITLE = {Theories with nonlocal electric charge
conservation},
JOURNAL = {Pisma Zh. \`Eksper. Teoret. Fiz.},
VOLUME = {34},
YEAR = {1981},
PAGES = {555--558},
URL = {http://jetpletters.ru/ps/1534/article_23455.pdf},
NOTE = {In Russian; translated in \textit{JETP
Letters} \textbf{34}: 10 (1981), 532--534.},
}
A. S. Schwarz :
“Supergravity, complex geometry and \( G \) -structures ,”
Comm. Math. Phys.
87 : 1
(1982 ),
pp. 37–63 .
MR
680647
Zbl
0503.53048
article
Abstract
BibTeX
@article {key680647m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Supergravity, complex geometry and \$G\$-structures},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {87},
NUMBER = {1},
YEAR = {1982},
PAGES = {37--63},
DOI = {10.1007/BF01211055},
URL = {http://projecteuclid.org/euclid.cmp/1103921903},
NOTE = {MR:680647. Zbl:0503.53048.},
ISSN = {0010-3616},
}
A. S. Schwarz :
“Field theories with no local conservation of the electric charge ,”
Nuclear Phys. B
208 : 1
(1982 ),
pp. 141–158 .
MR
682897
article
Abstract
BibTeX
@article {key682897m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Field theories with no local conservation
of the electric charge},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {208},
NUMBER = {1},
YEAR = {1982},
PAGES = {141--158},
DOI = {10.1016/0550-3213(82)90190-0},
NOTE = {MR:682897.},
ISSN = {0550-3213},
}
A. V. Gaĭduk, O. M. Khudaverdyan, and A. S. Shvarts :
“Integrirovanie po poverxnostqm v superprostranstve ”
[Integration over surfaces in superspace ],
Teor. Mat. Fiz.
52 : 3
(1982 ),
pp. 375–383 .
An English translation was published in Theor. Math. Phys. 52 :3 (1982) .
MR
692929
article
People
BibTeX
@article {key692929m,
AUTHOR = {Ga\u{\i}duk, A. V. and Khudaverdyan,
O. M. and Shvarts, A. S.},
TITLE = {Integrirovanie po poverxnostqm v superprostranstve
[Integration over surfaces in superspace]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {52},
NUMBER = {3},
YEAR = {1982},
PAGES = {375--383},
URL = {http://mi.mathnet.ru/tmf2560},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{52}:3
(1982). MR:692929.},
ISSN = {0564-6162},
}
A. S. Schwarz :
“A few remarks on the construction of solutions of nonlinear equations ,”
pp. 124–128
in
Twistor geometry and nonlinear systems
(Primorsko, Bulgaria, September 1980 ).
Edited by H.-D. Doebner and T. D. Palev .
Lecture Notes in Mathematics 970 .
Springer (Berlin ),
1982 .
MR
699804
Zbl
0522.47054
incollection
Abstract
People
BibTeX
@incollection {key699804m,
AUTHOR = {Schwarz, A. S.},
TITLE = {A few remarks on the construction of
solutions of nonlinear equations},
BOOKTITLE = {Twistor geometry and nonlinear systems},
EDITOR = {Doebner, Heinz-Dietrich and Palev, Tchavdar
D.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {970},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
PAGES = {124--128},
DOI = {10.1007/BFb0066027},
NOTE = {(Primorsko, Bulgaria, September 1980).
MR:699804. Zbl:0522.47054.},
ISSN = {0075-8434},
ISBN = {9783540119722},
}
V. A. Fateev, I. V. Frolov, and A. S. Schwarz :
“Grand unification and mirror particles ,”
Nuclear Phys. B
209 : 2
(December 1982 ),
pp. 427–432 .
article
Abstract
People
BibTeX
@article {key12704244,
AUTHOR = {Fateev, V. A. and Frolov, I. V. and
Schwarz, A. S.},
TITLE = {Grand unification and mirror particles},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {209},
NUMBER = {2},
MONTH = {December},
YEAR = {1982},
PAGES = {427--432},
DOI = {10.1016/0550-3213(82)90265-6},
ISSN = {0550-3213},
}
A. V. Gaĭduk, O. M. Khudaverdyan, and A. S. Shvarts :
“Integration over surfaces in superspace ,”
Theor. Math. Phys.
52 : 3
(1982 ),
pp. 862–868 .
English translation of Russian original published in Teor. Mat. Fiz. 52 :3 (1982) .
Zbl
0513.58015
article
Abstract
People
BibTeX
A study is made of \( (m,n) \) -densities, which are the most general entities that can be integrated over a \( (m,n) \) -dimensional surface in superspace. It is shown that the Bernshtein–Leites integral forms can be interpreted as densities; the class of densities corresponding to these forms is characterized.
@article {key0513.58015z,
AUTHOR = {Ga\u{\i}duk, A. V. and Khudaverdyan,
O. M. and Shvarts, A. S.},
TITLE = {Integration over surfaces in superspace},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical Mathematics and Physics},
VOLUME = {52},
NUMBER = {3},
YEAR = {1982},
PAGES = {862--868},
DOI = {10.1007/BF01038080},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{52}:3 (1982). Zbl:0513.58015.},
ISSN = {0040-5779},
}
O. M. Khudaverdyan and A. S. Shvarts :
“Normal gauge in supergravity ,”
Theor. Math. Phys.
57 : 3
(1983 ),
pp. 1189–1195 .
English translation of Russian original published in Teoret. Mat. Fiz. 57 :3 (1983) .
article
Abstract
People
BibTeX
@article {key82782293,
AUTHOR = {Khudaverdyan, O. M. and Shvarts, A.
S.},
TITLE = {Normal gauge in supergravity},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical Mathematics and Physics},
VOLUME = {57},
NUMBER = {3},
YEAR = {1983},
PAGES = {1189--1195},
DOI = {10.1007/BF01018745},
NOTE = {English translation of Russian original
published in \textit{Teoret. Mat. Fiz.}
\textbf{57}:3 (1983).},
ISSN = {0040-5779},
}
A. A. Roslyĭ and A. S. Schwarz :
“Geometriya neminimal’noj i al’ternativnoj minimal’noj superggravitatsii ”
[Geometry of nonminimal and alternative minimal supergravity ],
Yadernaya Fiz.
37 : 3
(1983 ),
pp. 786–794 .
An English translation was published in Soviet J. Nuclear Phys. 37 :3 (1983) .
MR
719875
article
People
BibTeX
@article {key719875m,
AUTHOR = {Rosly\u{\i}, A. A. and Schwarz, A. S.},
TITLE = {Geometriya neminimal\cprime noj i al\cprime
ternativnoj minimal\cprime noj superggravitatsii
[Geometry of nonminimal and alternative
minimal supergravity]},
JOURNAL = {Yadernaya Fiz.},
FJOURNAL = {Yadernaya Fizika. Akademiya Nauk SSSR},
VOLUME = {37},
NUMBER = {3},
YEAR = {1983},
PAGES = {786--794},
NOTE = {An English translation was published
in \textit{Soviet J. Nuclear Phys.}
\textbf{37}:3 (1983). MR:719875.},
ISSN = {0044-0027},
}
O. M. Khudaverdyan and A. S. Shvarts :
“Normal’naq kalibrovka v supergravitacii ”
[Normal gauge in supergravity ],
Teor. Mat. Fiz.
57 : 3
(1983 ),
pp. 354–362 .
An English translation was published in Theor. Math. Phys. 57 :3 (1983) .
MR
735394
article
People
BibTeX
@article {key735394m,
AUTHOR = {Khudaverdyan, O. M. and Shvarts, A.
S.},
TITLE = {Normal\cprime naq kalibrovka v supergravitacii
[Normal gauge in supergravity]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {57},
NUMBER = {3},
YEAR = {1983},
PAGES = {354--362},
URL = {http://mi.mathnet.ru/tmf2267},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{57}:3
(1983). MR:735394.},
ISSN = {0564-6162},
}
A. S. Shvarts :
“Elliptic operators in quantum field theory ,”
J. Soviet Math.
21 : 4
(March 1983 ),
pp. 551–601 .
English translation of Russian original published in Sovremennye Problemy Matematiki. Noveishie Dostizheniya 17 (1981) .
article
Abstract
BibTeX
@article {key27938261,
AUTHOR = {Shvarts, A. S.},
TITLE = {Elliptic operators in quantum field
theory},
JOURNAL = {J. Soviet Math.},
FJOURNAL = {Journal of Soviet Mathematics},
VOLUME = {21},
NUMBER = {4},
MONTH = {March},
YEAR = {1983},
PAGES = {551--601},
DOI = {10.1007/BF01084286},
NOTE = {English translation of Russian original
published in \textit{Sovremennye Problemy
Matematiki. Noveishie Dostizheniya}
\textbf{17} (1981).},
ISSN = {0090-4104},
}
A. A. Roslyĭ and A. S. Schwarz :
“Geometry of minimal and alternative minimal supergravity ,”
Soviet J. Nuclear Phys.
37 : 3
(1983 ),
pp. 466–471 .
English translation of Russian original published in Yadernaya Fiz. 37 :3 (1983) .
Zbl
0592.53067
article
Abstract
People
BibTeX
The geometry of \( N = 1 \) supergravity is investigated. It is proved, in particular, that the ”nongeometric” action of the alternative minimal supergravity can be obtained by means of a limiting process from the ”geometric” action of nonminimal supergravity. The methods used in this paper have general validity and are presumably applicable to an investigation of extended supergravity.
@article {key0592.53067z,
AUTHOR = {Rosly\u{\i}, A. A. and Schwarz, A. S.},
TITLE = {Geometry of minimal and alternative
minimal supergravity},
JOURNAL = {Soviet J. Nuclear Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {37},
NUMBER = {3},
YEAR = {1983},
PAGES = {466--471},
NOTE = {English translation of Russian original
published in \textit{Yadernaya Fiz.}
\textbf{37}:3 (1983). Zbl:0592.53067.},
ISSN = {0038-5506},
}
S. P. Novikov, Yu. M. Smirnov, and A. S. Shvarts :
“Vadim Arsen’evich Efremovich (k vos’midesqtiletiü so dnq rozhdeniq) ”
[Vadim Arsen’evich Efremovich (on his eightieth birthday) ],
Uspekhi Mat. Nauk
39 : 1(235)
(1984 ),
pp. 175–176 .
MR
733984
article
People
BibTeX
@article {key733984m,
AUTHOR = {Novikov, S. P. and Smirnov, Yu. M. and
Shvarts, A. S.},
TITLE = {Vadim {A}rsen\cprime evich {E}fremovich
(k vos\cprime midesqtileti\"u so dnq
rozhdeniq) [Vadim {A}rsen\cprime evich
{E}fremovich (on his eightieth birthday)]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {39},
NUMBER = {1(235)},
YEAR = {1984},
PAGES = {175--176},
URL = {http://mi.mathnet.ru/umn2239},
NOTE = {MR:733984.},
ISSN = {0042-1316},
}
M. A. Baranov and A. S. Shvarts :
“Characteristic classes of supergauge fields ”
[Xarakteristicheskie klassj superkalibrovochnjx poley ],
Funktsional. Anal. i Prilozhen.
18 : 2
(1984 ),
pp. 53–54 .
An English translation was published in Funct. Anal. Appl. 18 :2 (1984) .
MR
745700
Zbl
0559.53017
article
People
BibTeX
@article {key745700m,
AUTHOR = {Baranov, M. A. and Shvarts, A. S.},
TITLE = {Characteristic classes of supergauge
fields [Xarakteristicheskie klassj superkalibrovochnjx
poley]},
JOURNAL = {Funktsional. Anal. i Prilozhen.},
FJOURNAL = {Funktsional\cprime ny\u{\i} Analiz i
ego Prilozheniya. Akademiya Nauk SSSR},
VOLUME = {18},
NUMBER = {2},
YEAR = {1984},
PAGES = {53--54},
URL = {http://mi.mathnet.ru/faa1448},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{18}:2
(1984). MR:745700. Zbl:0559.53017.},
ISSN = {0374-1990},
}
A. S. Schwarz and Yu. S. Tyupkin :
“Quantization of antisymmetric tensors and Ray–Singer torsion ,”
Nuclear Phys. B
242 : 2
(1984 ),
pp. 436–446 .
MR
755845
article
Abstract
People
BibTeX
@article {key755845m,
AUTHOR = {Schwarz, A. S. and Tyupkin, Yu. S.},
TITLE = {Quantization of antisymmetric tensors
and {R}ay--{S}inger torsion},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {242},
NUMBER = {2},
YEAR = {1984},
PAGES = {436--446},
DOI = {10.1016/0550-3213(84)90403-6},
NOTE = {MR:755845.},
ISSN = {0550-3213},
}
M. A. Baranov and A. S. Shvarts :
“Kogomologii supermnogoobraziy ”
[Cohomology of supermanifolds ],
Funktsional. Anal. i Prilozhen.
18 : 3
(1984 ),
pp. 69–70 .
An English translation was published in Funct. Anal. Appl. 18 :3 (1984) .
MR
757252
article
People
BibTeX
@article {key757252m,
AUTHOR = {Baranov, M. A. and Shvarts, A. S.},
TITLE = {Kogomologii supermnogoobraziy [Cohomology
of supermanifolds]},
JOURNAL = {Funktsional. Anal. i Prilozhen.},
FJOURNAL = {Funktsional\cprime ny\u{\i} Analiz i
ego Prilozheniya. Akademiya Nauk SSSR},
VOLUME = {18},
NUMBER = {3},
YEAR = {1984},
PAGES = {69--70},
URL = {http://mi.mathnet.ru/faa1477},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{18}:3
(1984). MR:757252.},
ISSN = {0374-1990},
}
A. A. Rosly and A. S. Schwarz :
“Geometry of \( N=1 \) supergravity ,”
Comm. Math. Phys.
95 : 2
(1984 ),
pp. 161–184 .
MR
760330
Zbl
0644.53077
article
Abstract
People
BibTeX
@article {key760330m,
AUTHOR = {Rosly, A. A. and Schwarz, A. S.},
TITLE = {Geometry of \$N=1\$ supergravity},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {95},
NUMBER = {2},
YEAR = {1984},
PAGES = {161--184},
DOI = {10.1007/BF01468139},
NOTE = {MR:760330. Zbl:0644.53077.},
ISSN = {0010-3616},
}
A. S. Shvarts :
“On the definition of superspace ”
[K opredeleniü superprostranstva ],
Teor. Mat. Fiz.
60 : 1
(1984 ),
pp. 37–42 .
An English translation was published in Theor. Math. Phys. 60 :1 (1984) .
MR
760438
article
BibTeX
@article {key760438m,
AUTHOR = {Shvarts, A. S.},
TITLE = {On the definition of superspace [K opredeleni\"u
superprostranstva]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {60},
NUMBER = {1},
YEAR = {1984},
PAGES = {37--42},
URL = {http://mi.mathnet.ru/tmf5111},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{60}:1
(1984). MR:760438.},
ISSN = {0564-6162},
}
A. A. Rosly and A. S. Schwarz :
“Geometry of \( N=1 \) supergravity, II ,”
Comm. Math. Phys.
96 : 3
(1984 ),
pp. 285–309 .
MR
769349
Zbl
0644.53078
article
Abstract
People
BibTeX
The supergravity torsion and curvature constraints are shown to be a particular case of constraints arising in a general geometrical situation. For this purpose, a theorem is proved which describes the necessary and sufficient conditions that the given geometry can be realized on a surface as one induced by the geometry of the ambient space. The proof uses the theory of nonlinear partial differential equations in superspace, Spencer cohomologies, etc. This theorem generalizes various theorems, well known in mathematics (e.g., the Gauss–Codazzi theorem), and may be of its own interest.
@article {key769349m,
AUTHOR = {Rosly, A. A. and Schwarz, A. S.},
TITLE = {Geometry of \$N=1\$ supergravity, {II}},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {96},
NUMBER = {3},
YEAR = {1984},
PAGES = {285--309},
DOI = {10.1007/BF01214576},
URL = {http://projecteuclid.org/euclid.cmp/1103941851},
NOTE = {MR:769349. Zbl:0644.53078.},
ISSN = {0010-3616},
}
M. A. Baranov and A. S. Shvarts :
“Cohomology of supermanifolds ,”
Funct. Anal. Appl.
18 : 3
(1984 ),
pp. 236–238 .
English translation of Russian original published in Funktsional. Anal. i Prilozhen. 18 :3 (1984) .
Zbl
0555.58030
article
Abstract
People
BibTeX
Upon generalization to supermanifolds, the standard definition of cohomology groups of manifolds by means of the de Rham complex does not lead to interesting results. (The cohomology groups of supermanifolds so obtained are isomorphic with the cohomology groups of the underlying manifold.) In the present note we give different, less trivial generalizations of cohomology theory.
@article {key0555.58030z,
AUTHOR = {Baranov, M. A. and Shvarts, A. S.},
TITLE = {Cohomology of supermanifolds},
JOURNAL = {Funct. Anal. Appl.},
FJOURNAL = {Functional Analysis and Its Applications},
VOLUME = {18},
NUMBER = {3},
YEAR = {1984},
PAGES = {236--238},
DOI = {10.1007/BF01086162},
NOTE = {English translation of Russian original
published in \textit{Funktsional. Anal.
i Prilozhen.} \textbf{18}:3 (1984).
Zbl:0555.58030.},
ISSN = {0016-2663},
}
M. A. Baranov and A. S. Shvarts :
“Characteristic classes of supergauge fields ,”
Functional Analysis and its Applications
18 : 2
(1984 ),
pp. 130–132 .
English translation of Russian original published in Funktsional. Anal. i Prilozhen. 18 :2 (1984) .
Zbl
0573.53020
article
Abstract
People
BibTeX
In the present paper we shall construct the characteristic connection classes in vector fibers over a supermanifold, under the condition that, in a certain sense, the considered connection is not degenerate.
@article {key0573.53020z,
AUTHOR = {Baranov, M. A. and Shvarts, A. S.},
TITLE = {Characteristic classes of supergauge
fields},
JOURNAL = {Functional Analysis and its Applications},
FJOURNAL = {Funct. Anal. Appl.},
VOLUME = {18},
NUMBER = {2},
YEAR = {1984},
PAGES = {130--132},
DOI = {10.1007/BF01077824},
NOTE = {English translation of Russian original
published in \textit{Funktsional. Anal.
i Prilozhen.} \textbf{18}:2 (1984).
Zbl:0573.53020.},
ISSN = {0016-2663},
}
A. S. Shvarts :
“On the definition of superspace ,”
Theor. Math. Phys.
60 : 1
(1984 ),
pp. 657–660 .
English translation of Russian original published in Teor. Mat. Fiz. 60 :1 (1984) .
Zbl
0575.58005
article
Abstract
BibTeX
@article {key0575.58005z,
AUTHOR = {Shvarts, A. S.},
TITLE = {On the definition of superspace},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {60},
NUMBER = {1},
YEAR = {1984},
PAGES = {657--660},
DOI = {10.1007/BF01018248},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{60}:1 (1984). Zbl:0575.58005.},
ISSN = {0040-5779},
}
M. A. Baranov and A. S. Shvarts :
“Multiloop contribution to string theory ,”
JETP Lett.
42 : 8
(1985 ),
pp. 419–421 .
English translation of Russian original published in Pis’ma Zh. Eksper. Teoret. Fiz. 42 :8 (1985) .
article
Abstract
People
BibTeX
The contribution into string amplitudes from surfaces of arbitrary topology is calculated, which corresponds to the account of multiloop diagrams in the string theory. Formalism of the string theory, suggested by Polyakov, in which the calculation of loop contribution is reduced to the calculation of integrals according to a certain finite-dimensional superspace (superconformal space of \( V_{(f)} \) moduli is used). The measure of integration, appearing in the space, as well as the measure in its boson analog, appearing as a result of boson string analysis in critial dimensionality, are studied.
@article {key16232543,
AUTHOR = {Baranov, M. A. and Shvarts, A. S.},
TITLE = {Multiloop contribution to string theory},
JOURNAL = {JETP Lett.},
FJOURNAL = {JETP Letters},
VOLUME = {42},
NUMBER = {8},
YEAR = {1985},
PAGES = {419--421},
NOTE = {English translation of Russian original
published in \textit{Pis\cprime ma Zh.
Eksper. Teoret. Fiz.} \textbf{42}:8
(1985).},
ISSN = {0021-3640},
}
M. A. Baranov, A. A. Roslyĭ, and A. S. Shvarts :
“Superlightlike geodesics in supergravity ,”
Yadernaya Fiz.
41 : 1
(1985 ),
pp. 285–287 .
An English translation was published in Soviet J. Nuclear Phys. 41 :1 (1985) .
MR
804665
article
People
BibTeX
@article {key804665m,
AUTHOR = {Baranov, M. A. and Rosly\u{\i}, A. A.
and Shvarts, A. S.},
TITLE = {Superlightlike geodesics in supergravity},
JOURNAL = {Yadernaya Fiz.},
FJOURNAL = {Yadernaya Fizika. Akademiya Nauk SSSR},
VOLUME = {41},
NUMBER = {1},
YEAR = {1985},
PAGES = {285--287},
NOTE = {An English translation was published
in \textit{Soviet J. Nuclear Phys.}
\textbf{41}:1 (1985). MR:804665.},
ISSN = {0044-0027},
}
M. A. Baranov, A. A. Roslyĭ, and A. S. Shvarts :
“O svqzi gravitacii i supergravitacii ”
[On the connection between gravity and supergravity ],
Teoret. Mat. Fiz.
64 : 1
(1985 ),
pp. 7–16 .
An English translation was published in Theor. Math. Phys. 64 :1 (1985) .
MR
815093
article
People
BibTeX
@article {key815093m,
AUTHOR = {Baranov, M. A. and Rosly\u{\i}, A. A.
and Shvarts, A. S.},
TITLE = {O svqzi gravitacii i supergravitacii
[On the connection between gravity and
supergravity]},
JOURNAL = {Teoret. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {64},
NUMBER = {1},
YEAR = {1985},
PAGES = {7--16},
URL = {http://mi.mathnet.ru/tmf4897},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{64}:1
(1985). MR:815093.},
ISSN = {0564-6162},
}
A. A. Rosly and A. S. Schwarz :
“Geometrical origin of new unconstrained superfields ,”
pp. 308–324
in
Proceedings of the third seminar on quantum gravity
(Moscow, 23–25 October 1984 ).
Edited by M. A. Markov, V. A. Berezin, and V. P. Frolov .
World Scientific (Singapore ),
1985 .
MR
829729
incollection
Abstract
People
BibTeX
@incollection {key829729m,
AUTHOR = {Rosly, A. A. and Schwarz, A. S.},
TITLE = {Geometrical origin of new unconstrained
superfields},
BOOKTITLE = {Proceedings of the third seminar on
quantum gravity},
EDITOR = {Markov, M. A. and Berezin, V. A. and
Frolov, V. P.},
PUBLISHER = {World Scientific},
ADDRESS = {Singapore},
YEAR = {1985},
PAGES = {308--324},
NOTE = {(Moscow, 23--25 October 1984). MR:829729.},
ISBN = {9789971978907},
}
M. A. Baranov and A. S. Shvarts :
“O mnogopetlevom vklade v teoriyu struny ”
[Multiloop contribution to string theory ],
Pis’ma Zh. Eksper. Teoret. Fiz.
42 : 8
(1985 ),
pp. 340–342 .
An English translation was published in JETP Lett. 42 :8 (1985) .
MR
875755
article
People
BibTeX
@article {key875755m,
AUTHOR = {Baranov, M. A. and Shvarts, A. S.},
TITLE = {O mnogopetlevom vklade v teoriyu struny
[Multiloop contribution to string theory]},
JOURNAL = {Pis\cprime ma Zh. Eksper. Teoret. Fiz.},
FJOURNAL = {Pis\cprime ma v Zhurnal Eksperimental\cprime
no\u{\i} i Teoretichesko\u{\i} Fiziki},
VOLUME = {42},
NUMBER = {8},
YEAR = {1985},
PAGES = {340--342},
NOTE = {An English translation was published
in \textit{JETP Lett.} \textbf{42}:8
(1985). MR:875755.},
ISSN = {0370-274X},
}
M. A. Baranov, A. A. Roslyĭ, and A. S. Shvarts :
“Geometric aspects of supergravity ,”
Problemy Yadern. Fiz. i Kosm. Lucheĭ
24
(1985 ),
pp. 25–33 .
MR
887675
article
People
BibTeX
@article {key887675m,
AUTHOR = {Baranov, M. A. and Rosly\u{\i}, A. A.
and Shvarts, A. S.},
TITLE = {Geometric aspects of supergravity},
JOURNAL = {Problemy Yadern. Fiz. i Kosm. Luche\u{\i}},
FJOURNAL = {Problemy Yaderno\u{\i} Fiziki i Kosmicheskikh
Luche\u{\i}},
VOLUME = {24},
YEAR = {1985},
PAGES = {25--33},
NOTE = {MR:887675.},
ISSN = {0131-3142},
}
A. S. Schwarz and Yu. S. Tyupkin :
“Grand unification, strings, and mirror particles ,”
pp. 279–289
in
Group theoretical methods in physics
(Zvenigorod, USSR, 24–26 November 1982 ),
vol. 2 .
Edited by M. A. Markov, V. I. Man’ko, and A. E. Shabad .
Harwood Academic (Chur, Switzerland ),
1985 .
MR
989351
incollection
People
BibTeX
@incollection {key989351m,
AUTHOR = {Schwarz, A. S. and Tyupkin, Yu. S.},
TITLE = {Grand unification, strings, and mirror
particles},
BOOKTITLE = {Group theoretical methods in physics},
EDITOR = {Markov, M. A. and Man\cprime ko, V.
I. and Shabad, A. E.},
VOLUME = {2},
PUBLISHER = {Harwood Academic},
ADDRESS = {Chur, Switzerland},
YEAR = {1985},
PAGES = {279--289},
NOTE = {(Zvenigorod, USSR, 24--26 November 1982).
MR:989351.},
ISBN = {9783718602469},
}
M. A. Baranov, A. A. Roslyĭ, and A. S. Shvarts :
“On the connection between gravity and supergravity ,”
Theor. Math. Phys.
64 : 1
(1985 ),
pp. 649–655 .
English translation of Russian original published in Teoret. Mat. Fiz. 64 :1 (1985) .
Zbl
0584.53041
article
Abstract
People
BibTeX
@article {key0584.53041z,
AUTHOR = {Baranov, M. A. and Rosly\u{\i}, A. A.
and Shvarts, A. S.},
TITLE = {On the connection between gravity and
supergravity},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical Mathematics and Physics},
VOLUME = {64},
NUMBER = {1},
YEAR = {1985},
PAGES = {649--655},
DOI = {10.1007/BF01017031},
NOTE = {English translation of Russian original
published in \textit{Teoret. Mat. Fiz.}
\textbf{64}:1 (1985). Zbl:0584.53041.},
ISSN = {0040-5779},
}
M. A. Baranov, A. A. Roslyĭ, and A. S. Shvarts :
“Superlightlike geodesics in supergravity ,”
Soviet J. Nuclear Phys.
41 : 1
(1985 ),
pp. 285–287 .
English translation of Russian original published in Yadernaya Fiz. 41 :1 (1985) .
Zbl
0592.58013
article
Abstract
People
BibTeX
@article {key0592.58013z,
AUTHOR = {Baranov, M. A. and Rosly\u{\i}, A. A.
and Shvarts, A. S.},
TITLE = {Superlightlike geodesics in supergravity},
JOURNAL = {Soviet J. Nuclear Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {41},
NUMBER = {1},
YEAR = {1985},
PAGES = {285--287},
NOTE = {English translation of Russian original
published in \textit{Yadernaya Fiz.}
\textbf{41}:1 (1985). Zbl:0592.58013.},
ISSN = {0038-5506},
}
M. A. Baranov, Yu. I. Manin, I. V. Frolov, and A. S. Shvarts :
“Mnogopetlevoj vklad v fermionnoj strune ”
[The multiloop contribution in the fermion string ],
Yadernaya Fiz.
43 : 4
(1986 ),
pp. 1053–1056 .
An English translation was published in Soviet J. Nuclear Phys. 43 :4 (1986) .
article
People
BibTeX
@article {key80096976,
AUTHOR = {Baranov, M. A. and Manin, Yu. I. and
Frolov, I. V. and Shvarts, A. S.},
TITLE = {Mnogopetlevoj vklad v fermionnoj strune
[The multiloop contribution in the fermion
string]},
JOURNAL = {Yadernaya Fiz.},
FJOURNAL = {Yadernaya Fizika. Akademiya Nauk SSSR},
VOLUME = {43},
NUMBER = {4},
YEAR = {1986},
PAGES = {1053--1056},
NOTE = {An English translation was published
in \textit{Soviet J. Nuclear Phys.}
\textbf{43}:4 (1986).},
ISSN = {0044-0027},
}
A. A. Rosly and A. S. Schwarz :
“Supersymmetry in a space with auxiliary dimensions ,”
Comm. Math. Phys.
105 : 4
(1986 ),
pp. 645–668 .
MR
852094
article
Abstract
People
BibTeX
@article {key852094m,
AUTHOR = {Rosly, A. A. and Schwarz, A. S.},
TITLE = {Supersymmetry in a space with auxiliary
dimensions},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {105},
NUMBER = {4},
YEAR = {1986},
PAGES = {645--668},
DOI = {10.1007/BF01238937},
NOTE = {MR:852094.},
ISSN = {0010-3616},
}
M. A. Baranov, Yu. I. Manin, I. V. Frolov, and A. S. Shvarts :
“The multiloop contribution in the fermion string ,”
Soviet J. Nuclear Phys.
43 : 4
(1986 ),
pp. 670–671 .
English translation of Russian original published in Yadernaya Fiz. 43 :4 (1986) .
MR
857425
article
Abstract
People
BibTeX
@article {key857425m,
AUTHOR = {Baranov, M. A. and Manin, Yu. I. and
Frolov, I. V. and Shvarts, A. S.},
TITLE = {The multiloop contribution in the fermion
string},
JOURNAL = {Soviet J. Nuclear Phys.},
FJOURNAL = {Soviet Journal of Nuclear Physics},
VOLUME = {43},
NUMBER = {4},
YEAR = {1986},
PAGES = {670--671},
NOTE = {English translation of Russian original
published in \textit{Yadernaya Fiz.}
\textbf{43}:4 (1986). MR:857425.},
ISSN = {0038-5506},
}
A. A. Roslyĭ, O. M. Khudaverdyan, and A. S. Shvarts :
“Supersimmetriq i kompleksnaq geometriq ”
[Supersymmetry and complex geometry ],
pp. 247–284
in
Complex analysis: Several variables, III .
Edited by G. M. Khenkin and R. V. Gamkrelidze .
Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya 9 .
VINITI (Moscow ),
1986 .
An English translation was published in 1989 .
MR
860614
incollection
People
BibTeX
@incollection {key860614m,
AUTHOR = {Rosly\u{\i}, A. A. and Khudaverdyan,
O. M. and Shvarts, A. S.},
TITLE = {Supersimmetriq i kompleksnaq geometriq
[Supersymmetry and complex geometry]},
BOOKTITLE = {Complex analysis: {S}everal variables,
{III}},
EDITOR = {Khenkin, G. M. and Gamkrelidze, R. V.},
SERIES = {Sovremennye Problemy Matematiki. Fundamental\cprime
nye Napravleniya},
NUMBER = {9},
PUBLISHER = {VINITI},
ADDRESS = {Moscow},
YEAR = {1986},
PAGES = {247--284},
URL = {http://mi.mathnet.ru/eng/intf63},
NOTE = {An English translation was published
in 1989. MR:860614.},
ISSN = {0202-7488},
}
M. A. Baranov, I. V. Frolov, and A. S. Shvarts :
“Geometriya dvumernykh superkonformnykh teorij polya ”
[Geometry of two-dimensional superconformal field theories ],
Teor. Mat. Fiz.
70 : 1
(1987 ),
pp. 92–103 .
An English translation was published in Theor. Math. Phys. 70 :1 (1987) .
MR
883786
Zbl
0624.58002
article
People
BibTeX
@article {key883786m,
AUTHOR = {Baranov, M. A. and Frolov, I. V. and
Shvarts, A. S.},
TITLE = {Geometriya dvumernykh superkonformnykh
teorij polya [Geometry of two-dimensional
superconformal field theories]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {70},
NUMBER = {1},
YEAR = {1987},
PAGES = {92--103},
URL = {http://mi.mathnet.ru/tmf4497},
NOTE = {An English translation was published
in \textit{Theor. Math. Phys.} \textbf{70}:1
(1987). MR:883786. Zbl:0624.58002.},
ISSN = {0564-6162},
}
A. M. Baranov, Yu. I. Manin, I. V. Frolov, and A. S. Schwarz :
“A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings ,”
Comm. Math. Phys.
111 : 3
(1987 ),
pp. 373–392 .
MR
900500
Zbl
0624.58033
article
Abstract
People
BibTeX
@article {key900500m,
AUTHOR = {Baranov, A. M. and Manin, Yu. I. and
Frolov, I. V. and Schwarz, A. S.},
TITLE = {A superanalog of the {S}elberg trace
formula and multiloop contributions
for fermionic strings},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {111},
NUMBER = {3},
YEAR = {1987},
PAGES = {373--392},
DOI = {10.1007/BF01238904},
NOTE = {MR:900500. Zbl:0624.58033.},
ISSN = {0010-3616},
}
M. A. Baranov and A. S. Schwarz :
“On the multiloop contribution to the string theory ,”
Internat. J. Modern Phys. A
2 : 6
(1987 ),
pp. 1773–1796 .
MR
913613
article
Abstract
People
BibTeX
The supermoduli space and the measure on this space arising from fermionic string theory are studied. Analytic properties of this measure are analyzed. Our considerations, combined with previous results by Voronov, give an expression of string measure through analytic superfields and their zeros. The behavior of measure in the vicinity of the boundary of moduli space is studied on the base of this expression.
@article {key913613m,
AUTHOR = {Baranov, M. A. and Schwarz, A. S.},
TITLE = {On the multiloop contribution to the
string theory},
JOURNAL = {Internat. J. Modern Phys. A},
FJOURNAL = {International Journal of Modern Physics
A. Particles and Fields. Gravitation.
Cosmology},
VOLUME = {2},
NUMBER = {6},
YEAR = {1987},
PAGES = {1773--1796},
DOI = {10.1142/S0217751X87000922},
NOTE = {MR:913613.},
ISSN = {0217-751X},
}
A. S. Shvarts :
“The fermion string and a universal modulus space ,”
JETP Lett.
46 : 9
(1987 ),
pp. 428–431 .
English translation of Russian original published in Pis’ma Zh. Èksper. Teoret. Fiz. 46 :9 (1987) .
MR
940601
article
BibTeX
@article {key940601m,
AUTHOR = {Shvarts, A. S.},
TITLE = {The fermion string and a universal modulus
space},
JOURNAL = {JETP Lett.},
FJOURNAL = {JETP Letters},
VOLUME = {46},
NUMBER = {9},
YEAR = {1987},
PAGES = {428--431},
NOTE = {English translation of Russian original
published in \textit{Pis\cprime ma Zh.
\`Eksper. Teoret. Fiz.} \textbf{46}:9
(1987). MR:940601.},
ISSN = {0021-3640},
}
A. S. Schwarz and Yu. S. Tyupkin :
“Measurement theory and the Schrödinger equation ,”
pp. 667–675
in
Quantum field theory and quantum statistics: Essays in honour of the sixtieth birthday of E. S. Fradkin ,
vol. 1 .
Edited by I. A. Batalin, C. J. Isham, and G. A. Vilkovisky .
Hilger (Bristol, UK ),
1987 .
MR
943165
incollection
People
BibTeX
@incollection {key943165m,
AUTHOR = {Schwarz, A. S. and Tyupkin, Yu. S.},
TITLE = {Measurement theory and the {S}chr\"odinger
equation},
BOOKTITLE = {Quantum field theory and quantum statistics:
{E}ssays in honour of the sixtieth birthday
of {E}.~{S}. {F}radkin},
EDITOR = {Batalin, I. A. and Isham, C. J. and
Vilkovisky, G. A.},
VOLUME = {1},
PUBLISHER = {Hilger},
ADDRESS = {Bristol, UK},
YEAR = {1987},
PAGES = {667--675},
NOTE = {MR:943165.},
ISBN = {9780852745748},
}
A. S. Shvarts :
“Fermionnaya struna i universal’noe prostranstvo modulej ”
[The fermion string and a universal modulus space ],
Pis’ma Zh. Eksper. Teoret. Fiz.
46 : 9
(1987 ),
pp. 340–342 .
An English translation of was published in JETP Lett. 46 :9 (1987) .
article
BibTeX
@article {key15018842,
AUTHOR = {Shvarts, A. S.},
TITLE = {Fermionnaya struna i universal'noe prostranstvo
modulej [The fermion string and a universal
modulus space]},
JOURNAL = {Pis\cprime ma Zh. Eksper. Teoret. Fiz.},
FJOURNAL = {Pis\cprime ma v Zhurnal Eksperimental\cprime
no\u{\i} i Teoretichesko\u{\i} Fiziki},
VOLUME = {46},
NUMBER = {9},
YEAR = {1987},
PAGES = {340--342},
NOTE = {An English translation of was published
in \textit{JETP Lett.} \textbf{46}:9
(1987).},
ISSN = {0370-274X},
}
M. A. Baranov, I. V. Frolov, and A. S. Shvarts :
“Geometry of superconformal field theories in two dimensions ,”
Theor. Math. Phys.
70 : 1
(1987 ),
pp. 64–72 .
English translation of Russian original published in Teor. Mat. Fiz. 70 :1 (1987) .
article
Abstract
People
BibTeX
@article {key58345010,
AUTHOR = {Baranov, M. A. and Frolov, I. V. and
Shvarts, A. S.},
TITLE = {Geometry of superconformal field theories
in two dimensions},
JOURNAL = {Theor. Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {70},
NUMBER = {1},
YEAR = {1987},
PAGES = {64--72},
DOI = {10.1007/BF01017011},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{70}:1 (1987).},
ISSN = {0040-5779},
}
A. Schwarz and M. Baranov :
Superconformal geometry and multiloop contribution to the string theory .
Preprint ,
MIFI (Moscow) ,
1987 .
techreport
People
BibTeX
@techreport {key68463700,
AUTHOR = {Schwarz, A.S. and M. Baranov},
TITLE = {Superconformal geometry and multiloop
contribution to the string theory},
TYPE = {preprint},
INSTITUTION = {MIFI (Moscow)},
YEAR = {1987},
PAGES = {011-87, 21 pages},
}
A. A. Rosly, A. S. Schwarz, and A. A. Voronov :
“Geometry of superconformal manifolds ,”
Comm. Math. Phys.
119 : 1
(1988 ),
pp. 129–152 .
MR
968484
Zbl
0675.58010
article
Abstract
People
BibTeX
The main facts about complex curves are generalized to superconformal manifolds. The results thus obtained are relevant to the fermion string theory and, in particular, they are useful for computation of determinants of super laplacians which enter the string partition function.
@article {key968484m,
AUTHOR = {Rosly, A. A. and Schwarz, A. S. and
Voronov, Alexander A.},
TITLE = {Geometry of superconformal manifolds},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {119},
NUMBER = {1},
YEAR = {1988},
PAGES = {129--152},
DOI = {10.1007/BF01218264},
NOTE = {MR:968484. Zbl:0675.58010.},
ISSN = {0010-3616},
}
A. A. Rosly, A. S. Schwarz, and A. A. Voronov :
“Superconformal geometry and string theory ,”
Comm. Math. Phys.
120 : 3
(1989 ),
pp. 437–450 .
MR
981212
Zbl
0667.58008
article
Abstract
People
BibTeX
@article {key981212m,
AUTHOR = {Rosly, A. A. and Schwarz, A. S. and
Voronov, Alexander A.},
TITLE = {Superconformal geometry and string theory},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {120},
NUMBER = {3},
YEAR = {1989},
PAGES = {437--450},
DOI = {10.1007/BF01225506},
NOTE = {MR:981212. Zbl:0667.58008.},
ISSN = {0010-3616},
}
A. S. Schwarz :
“Fermionic string and universal moduli space ,”
Nuclear Phys. B
317 : 2
(1989 ),
pp. 323–343 .
MR
1001895
article
Abstract
BibTeX
@article {key1001895m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Fermionic string and universal moduli
space},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {317},
NUMBER = {2},
YEAR = {1989},
PAGES = {323--343},
DOI = {10.1016/0550-3213(89)90072-2},
NOTE = {MR:1001895.},
ISSN = {0550-3213},
}
M. A. Baranov, I. V. Frolov, and A. S. Schwarz :
“Geometriq superkonformnogo prostranstva moduley ”
[Geometry of the superconformal moduli space ],
Teor. Mat. Fiz.
79 : 2
(1989 ),
pp. 241–252 .
An English translation was published in Theoret. and Math. Phys. 79 :2 (1989) .
MR
1007798
Zbl
0679.53058
article
People
BibTeX
@article {key1007798m,
AUTHOR = {Baranov, M. A. and Frolov, I. V. and
Schwarz, A. S.},
TITLE = {Geometriq superkonformnogo prostranstva
moduley [Geometry of the superconformal
moduli space]},
JOURNAL = {Teor. Mat. Fiz.},
FJOURNAL = {Teoreticheskaya i Matematicheskaya Fizika.
Akademiya Nauk SSSR},
VOLUME = {79},
NUMBER = {2},
YEAR = {1989},
PAGES = {241--252},
URL = {http://mi.mathnet.ru/tmf4873},
NOTE = {An English translation was published
in \textit{Theoret. and Math. Phys.}
\textbf{79}:2 (1989). MR:1007798. Zbl:0679.53058.},
ISSN = {0564-6162},
}
A. S. Schwarz :
“Statistics of skyrmions ,”
Mod. Phys. Lett. A
4 : 4
(1989 ),
pp. 403–407 .
MR
1016533
article
Abstract
BibTeX
@article {key1016533m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Statistics of skyrmions},
JOURNAL = {Mod. Phys. Lett. A},
FJOURNAL = {Modern Physics Letters A},
VOLUME = {4},
NUMBER = {4},
YEAR = {1989},
PAGES = {403--407},
DOI = {10.1142/S0217732389000484},
NOTE = {MR:1016533.},
ISSN = {0217-7323},
}
A. S. Schwarz :
“Lefschetz trace formula and BRST ,”
Modern Phys. Lett. A
4 : 20
(1989 ),
pp. 1891–1897 .
MR
1023771
article
Abstract
BibTeX
@article {key1023771m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Lefschetz trace formula and {BRST}},
JOURNAL = {Modern Phys. Lett. A},
FJOURNAL = {Modern Physics Letters A},
VOLUME = {4},
NUMBER = {20},
YEAR = {1989},
PAGES = {1891--1897},
DOI = {10.1142/S0217732389002148},
NOTE = {MR:1023771.},
ISSN = {0217-7323},
}
A. S. Shvarts :
Kvantovaya teoriya polya i topologiya
[Quantum field theory and topology ].
Nauka (Moscow ),
1989 .
An English translation was published in 1993 .
Zbl
0682.58001
book
BibTeX
@book {key0682.58001z,
AUTHOR = {Shvarts, A. S.},
TITLE = {Kvantovaya teoriya polya i topologiya
[Quantum field theory and topology]},
PUBLISHER = {Nauka},
ADDRESS = {Moscow},
YEAR = {1989},
PAGES = {400},
NOTE = {An English translation was published
in 1993. Zbl:0682.58001.},
}
M. A. Baranov, I. V. Frolov, and A. S. Schwarz :
“Geometry of the superconformal moduli space ,”
Theoret. and Math. Phys.
79 : 2
(May 1989 ),
pp. 509–517 .
English translation of Russian original published in Teor. Mat. Fiz. 79 :2 (1989) .
Zbl
0694.53060
article
Abstract
People
BibTeX
The geometry of the moduli space of superconformal manifolds is studied in the case when the underlying manifold is compact or differs from a compact manifold by the deletion of some points. In particular, it is shown that the superanalog of the Weyl–Peterson metric is Kählerian, and the corresponding measure on the superconformal moduli space is calculated.
@article {key0694.53060z,
AUTHOR = {Baranov, M. A. and Frolov, I. V. and
Schwarz, A. S.},
TITLE = {Geometry of the superconformal moduli
space},
JOURNAL = {Theoret. and Math. Phys.},
FJOURNAL = {Theoretical and Mathematical Physics},
VOLUME = {79},
NUMBER = {2},
MONTH = {May},
YEAR = {1989},
PAGES = {509--517},
DOI = {10.1007/BF01016532},
NOTE = {English translation of Russian original
published in \textit{Teor. Mat. Fiz.}
\textbf{79}:2 (1989). Zbl:0694.53060.},
ISSN = {0040-5779},
}
A. A. Roslyĭ, O. M. Khudaverdyan, and A. S. Shvarts :
“Supersymmetry and complex geometry ,”
pp. 223–261
in
Several complex variables, III: Geometric function theory .
Edited by G. M. Khenkin and R. V. Gamkrelidze .
Enclyclopedia of the Mathematical Sciences 9 .
Springer (Berlin ),
1989 .
English translation of Russian original published in 1986 .
Zbl
0794.53050
incollection
Abstract
People
BibTeX
In the past years supersymmetric theories have gained great importance in physics. By this one intends field theoretical models based on a new form of symmetry dubbed supersymmetry. Supersymmetry connects boson and fermion fields with each other [Gayduk et al. 1981; Volkov and Akulov 1974; Wess 1978; Ogievetskii and Mezinchesku 1975; Fayet and Ferrara 1977]. The observed properties of particles cannot satisfy the demands of supersymmetry (for instance, supersymmetry would lead to the equality of mass for the boson and the corresponding fermion). However, an increasing number of physicists have arrived at the conviction that the action functional of interactions encountered in nature must be supersymmetrical (although for the ground state (the physical vacuum) and, consequently, for the observed spectra of particles supersymmetry is broken). Perhaps the most weighty foundation for such a belief is the mathematical beauty of the supersymmetric theories and the remarkable property of cancellation of the divergencies appearing in these theories. It is question of the circumstance that in quantum field theories one encounters divergencies arising from the integration over large momenta (ultraviolet divergencies). In supersymmetry the most dangerous of these divergencies cancel. Moreover, there exist models completely free of ultraviolet divergencies. Presently great hopes are put on such supersymmetric theories which take account of the presence of gravitational interactions. Thus an important constituent part of these theories is played by supergravity , a supersymmetric theory containing Einstein’s theory of gravity.
@incollection {key0794.53050z,
AUTHOR = {Rosly\u{\i}, A. A. and Khudaverdyan,
O. M. and Shvarts, A. S.},
TITLE = {Supersymmetry and complex geometry},
BOOKTITLE = {Several complex variables, {III}: {G}eometric
function theory},
EDITOR = {Khenkin, G. M. and Gamkrelidze, R. V.},
SERIES = {Enclyclopedia of the Mathematical Sciences},
NUMBER = {9},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1989},
PAGES = {223--261},
DOI = {10.1007/978-3-642-61308-1_7},
NOTE = {English translation of Russian original
published in 1986. Zbl:0794.53050.},
ISSN = {0938-0396},
ISBN = {9783540170051},
}
A. S. Schwarz :
“New topological invariants arising in the theory of quantized fields ”
in
Baku International Topological Conference, abstracts
(Baku, October 3–9, 1987 ).
Edited by B. R. Nuriev .
Elm (Baku, Azerbaijan ),
1989 .
MR
1347199
inproceedings
BibTeX
@inproceedings {key1347199m,
AUTHOR = {Schwarz, A. S.},
TITLE = {New topological invariants arising in
the theory of quantized fields},
BOOKTITLE = {Baku International Topological Conference,
abstracts},
EDITOR = {Nuriev, B. R.},
PUBLISHER = {Elm},
ADDRESS = {Baku, Azerbaijan},
YEAR = {1989},
NOTE = {(Baku, October 3--9, 1987). MR:1347199.},
}
H. La, P. Nelson, and A. S. Schwarz :
“Virasoro model space ,”
Comm. Math. Phys.
134 : 3
(December 1990 ),
pp. 539–554 .
MR
1086743
article
Abstract
People
BibTeX
The representations of a compact Lie group \( G \) can be studied via the construction of an associated “model space”. This space has the property that when geometrically quantized its Hilbert space contains every irreducible representation of \( G \) just once. We construct an analogous space for the group \( \operatorname{Diff} S^1 \) . It is naturally a complex manifold with a holomorphic, free action of \( \operatorname{Diff} S^1 \) preserving a family of pseudo-Kahler structures. All of the “good” coadjoint orbits are obtained from our space by Hamiltonian constraint reduction. We briefly discuss the connection to the work of Alekseev and Shatashvili.
@article {key1086743m,
AUTHOR = {La, HoSeong and Nelson, Philip and Schwarz,
A. S.},
TITLE = {Virasoro model space},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {134},
NUMBER = {3},
MONTH = {December},
YEAR = {1990},
PAGES = {539--554},
DOI = {10.1007/BF02098446},
NOTE = {MR:1086743.},
ISSN = {0010-3616},
}
V. S. Makarov, A. A. Mal’tsev, S. P. Novikov, S. S. Ryshkov, E. S. Tikhomirova, and A. S. Shvarts :
“Vadim Arsenievich Efremovich (obituary) ”
[Efremovich Vadim Arsen’evich (nekrolog) ],
Uspekhi Mat. Nauk
45 : 6(276)
(1990 ),
pp. 113–114 .
An English translation was published in Russ. Math. Surv. 45 :6 (1990) .
MR
1101334
article
People
BibTeX
@article {key1101334m,
AUTHOR = {Makarov, V. S. and Mal\cprime tsev,
A. A. and Novikov, S. P. and Ryshkov,
S. S. and Tikhomirova, E. S. and Shvarts,
A. S.},
TITLE = {Vadim {A}rsenievich {E}fremovich (obituary)
[Efremovich {V}adim {A}rsen\cprime evich
(nekrolog)]},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {45},
NUMBER = {6(276)},
YEAR = {1990},
PAGES = {113--114},
URL = {http://mi.mathnet.ru/umn4808},
NOTE = {An English translation was published
in \textit{Russ. Math. Surv.} \textbf{45}:6
(1990). MR:1101334.},
ISSN = {0042-1316},
}
S. N. Dolgikh and A. S. Schwarz :
“Supergrassmannians, super \( \tau \) -functions and strings ,”
pp. 231–244
in
Physics and mathematics of strings: Memorial volume for Vadim Knizhik .
Edited by L. Brink, D. Friedan, and A. M. Polyakov .
World Scientific (Teaneck, NJ ),
1990 .
MR
1104261
Zbl
0737.58056
incollection
Abstract
People
BibTeX
@incollection {key1104261m,
AUTHOR = {Dolgikh, S. N. and Schwarz, A. S.},
TITLE = {Supergrassmannians, super \$\tau\$-functions
and strings},
BOOKTITLE = {Physics and mathematics of strings:
{M}emorial volume for {V}adim {K}nizhik},
EDITOR = {Brink, L. and Friedan, D. and Polyakov,
A. M.},
PUBLISHER = {World Scientific},
ADDRESS = {Teaneck, NJ},
YEAR = {1990},
PAGES = {231--244},
NOTE = {MR:1104261. Zbl:0737.58056.},
ISBN = {9789971509804},
}
A. S. Schwarz :
“Universal moduli space and string theory ,”
pp. 450–456
in
Superstrings ’89
(Trieste, Italy, 3–14 April 1989 ).
Edited by M. Green, R. Iengo, S. Randjbar-Daemi, E. Sezgin, and A. Strominger .
World Scientific (Singapore ),
1990 .
MR
1159976
Zbl
0985.81680
incollection
Abstract
People
BibTeX
@incollection {key1159976m,
AUTHOR = {Schwarz, A. S.},
TITLE = {Universal moduli space and string theory},
BOOKTITLE = {Superstrings '89},
EDITOR = {Green, M. and Iengo, R. and Randjbar-Daemi,
S. and Sezgin, E. and Strominger, A.},
PUBLISHER = {World Scientific},
ADDRESS = {Singapore},
YEAR = {1990},
PAGES = {450--456},
NOTE = {(Trieste, Italy, 3--14 April 1989).
MR:1159976. Zbl:0985.81680.},
ISBN = {9789810201388},
}
V. S. Makarov, A. A. Mal’tsev, S. P. Novikov, S. S. Ryshkov, E. S. Tikhomirova, and A. S. Shvarts :
“Vadim Arsenievich Efremovich (obituary) ,”
Russ. Math. Surv.
45 : 6
(December 1990 ),
pp. 137–138 .
English translation of Russian original published in Uspekhi Mat. Nauk 45 :6(276) (1990) .
article
People
BibTeX
@article {key94586638,
AUTHOR = {Makarov, V. S. and Mal\cprime tsev,
A. A. and Novikov, S. P. and Ryshkov,
S. S. and Tikhomirova, E. S. and Shvarts,
A. S.},
TITLE = {Vadim {A}rsenievich {E}fremovich (obituary)},
JOURNAL = {Russ. Math. Surv.},
FJOURNAL = {Russian Mathematical Surveys},
VOLUME = {45},
NUMBER = {6},
MONTH = {December},
YEAR = {1990},
PAGES = {137--138},
DOI = {10.1070/RM1990v045n06ABEH002696},
NOTE = {English translation of Russian original
published in \textit{Uspekhi Mat. Nauk}
\textbf{45}:6(276) (1990).},
ISSN = {0036-0279},
}
A. Schwarz :
Symplectic, contact and superconformal geometry, membranes and strings .
Preprint 90-12 ,
1990 .
techreport
BibTeX
@techreport {key13345503,
AUTHOR = {Schwarz, A.},
TITLE = {Symplectic, contact and superconformal
geometry, membranes and strings},
TYPE = {Preprint},
NUMBER = {90-12},
YEAR = {1990},
}
S. N. Dolgikh, A. A. Rosly, and A. S. Schwarz :
“Supermoduli spaces ,”
Commun. Math. Phys.
135 : 1
(1990 ),
pp. 91–100 .
MR
1086753
Zbl
0715.32008
article
Abstract
People
BibTeX
@article {key1086753m,
AUTHOR = {Dolgikh, S. N. and Rosly, A. A. and
Schwarz, A. S.},
TITLE = {Supermoduli spaces},
JOURNAL = {Commun. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {135},
NUMBER = {1},
YEAR = {1990},
PAGES = {91--100},
DOI = {10.1007/BF02097658},
NOTE = {MR:1086753. Zbl:0715.32008.},
ISSN = {0010-3616},
}
A. Schwarz :
“On some mathematical problems of 2D-gravity and \( W_h \) -gravity ,”
Mod. Phys. Lett. A
6 : 7
(1991 ),
pp. 611–616 .
MR
1098645
Zbl
1020.37578
article
Abstract
BibTeX
@article {key1098645m,
AUTHOR = {Schwarz, Albert},
TITLE = {On some mathematical problems of 2{D}-gravity
and \$W_h\$-gravity},
JOURNAL = {Mod. Phys. Lett. A},
FJOURNAL = {Modern Physics Letters A},
VOLUME = {6},
NUMBER = {7},
YEAR = {1991},
PAGES = {611--616},
DOI = {10.1142/S0217732391000634},
NOTE = {MR:1098645. Zbl:1020.37578.},
ISSN = {0217-7323},
}
V. Kac and A. Schwarz :
“Geometric interpretation of the partition function of 2D gravity ,”
Phys. Lett. B
257 : 3–4
(1991 ),
pp. 329–334 .
MR
1100639
article
Abstract
People
BibTeX
@article {key1100639m,
AUTHOR = {Kac, V. and Schwarz, A.},
TITLE = {Geometric interpretation of the partition
function of 2{D} gravity},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters B},
VOLUME = {257},
NUMBER = {3--4},
YEAR = {1991},
PAGES = {329--334},
DOI = {10.1016/0370-2693(91)91901-7},
NOTE = {MR:1100639.},
ISSN = {0370-2693},
}
A. Schwarz :
“On solutions to the string equation ,”
Mod. Phys. Lett. A
6 : 29
(1991 ),
pp. 2713–2725 .
MR
1126806
Zbl
1020.37579
ArXiv
hep-th/9109015
article
Abstract
BibTeX
@article {key1126806m,
AUTHOR = {Schwarz, Albert},
TITLE = {On solutions to the string equation},
JOURNAL = {Mod. Phys. Lett. A},
FJOURNAL = {Modern Physics Letters A},
VOLUME = {6},
NUMBER = {29},
YEAR = {1991},
PAGES = {2713--2725},
DOI = {10.1142/S0217732391003171},
NOTE = {ArXiv:hep-th/9109015. MR:1126806. Zbl:1020.37579.},
ISSN = {0217-7323},
}
A. S. Schwarz and A. Sen :
“Gluing theorem, star product and integration in open string field theory in arbitrary background fields ,”
Int. J. Mod. Phys. A
6 : 30
(1991 ),
pp. 5387–5407 .
MR
1137572
Zbl
0802.53032
article
Abstract
People
BibTeX
@article {key1137572m,
AUTHOR = {Schwarz, A. S. and Sen, Ashoke},
TITLE = {Gluing theorem, star product and integration
in open string field theory in arbitrary
background fields},
JOURNAL = {Int. J. Mod. Phys. A},
FJOURNAL = {International Journal of Modern Physics
A},
VOLUME = {6},
NUMBER = {30},
YEAR = {1991},
PAGES = {5387--5407},
DOI = {10.1142/S0217751X91002537},
NOTE = {MR:1137572. Zbl:0802.53032.},
ISSN = {0217-751X},
}
A. Schwarz :
“Geometry of fermionic string ,”
pp. 1377–1386
in
Proceedings of the International Congress of Mathematicians
(Kyoto, Japan, 21–29 August 1990 ),
vol. 2 .
Edited by I. Satake .
Springer (Tokyo ),
1991 .
MR
1159322
Zbl
0751.53024
incollection
Abstract
People
BibTeX
Physicists hope that the Green–Schwarz superstring theory describes all interactions existing in the Nature. However the verification of this conjecture is connected with very difficult and very interesting mathematical problems. We consider here only some problems arising in the Polyakov approach to the fermionic string. (Fermionic string is closely related with the Green–Schwarz superstring.) We explain the connection between string theory and superconformal geometry, the origin of string measure on superconformal moduli space and analytic properties of this measure, the construction of universal moduli space and the expression of string measure in terms of super \( \tau \) -function etc. The lecture is based on the papers [Baranov and Schwarz 1985; Baranov, Frolov and Schwarz 1987; Baranov and Schwarz 1987; Schwarz 1988; Rosly, Schwarz and Voronov 1988; Rosly, Schwarz and Voronov 1989; Schwarz 1989; Dolgikh and Schwarz 1990; Dolgikh, Rosly and Schwarz 1990; Baranov, Frolov and Schwarz 1989]. The results concerning the measure on the moduli space of \( N = 2 \) superconformal manifolds are new.
@incollection {key1159322m,
AUTHOR = {Schwarz, Albert},
TITLE = {Geometry of fermionic string},
BOOKTITLE = {Proceedings of the {I}nternational {C}ongress
of {M}athematicians},
EDITOR = {Satake, Ichiro},
VOLUME = {2},
PUBLISHER = {Springer},
ADDRESS = {Tokyo},
YEAR = {1991},
PAGES = {1377--1386},
NOTE = {(Kyoto, Japan, 21--29 August 1990).
MR:1159322. Zbl:0751.53024.},
ISBN = {9784431700470},
}
H. La, P. Nelson, and A. S. Schwarz :
“Remarks on Virasoro model space ,”
pp. 259–265
in
Strings ’90
(College Station, TX, 21–17 March 1990 ).
Edited by R. Arnowitt, R. Bryan, M. J. Duff, D. V. Nanopoulos, C. N. Pope, and E. Sezgin .
World Scientific (River Edge, NJ ),
1991 .
MR
1256501
incollection
Abstract
People
BibTeX
@incollection {key1256501m,
AUTHOR = {La, HoSeong and Nelson, Philip and Schwarz,
A. S.},
TITLE = {Remarks on {V}irasoro model space},
BOOKTITLE = {Strings '90},
EDITOR = {Arnowitt, R. and Bryan, R. and Duff,
M. J. and Nanopoulos, D. V. and Pope,
C. N. and Sezgin, E.},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {1991},
PAGES = {259--265},
NOTE = {(College Station, TX, 21--17 March 1990).
MR:1256501.},
ISBN = {9789814520072},
}
K. N. Anagnostopoulos, M. J. Bowick, and A. Schwarz :
“The solution space of the unitary matrix model string equation and the Sato Grassmannian ,”
Commun. Math. Phys.
148 : 3
(1992 ),
pp. 469–485 .
MR
1181066
Zbl
0753.35073
ArXiv
hep-th/9112066
article
Abstract
People
BibTeX
The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points \( V_1 \) and \( V_2 \) in the big cell \( \mathrm{Gr}^{(0)} \) of the Sato Grassmannian \( \mathrm{Gr} \) . This is a consequence of a well-defined continuum limit in which the string equation has the simple form \( [\mathscr{P},\mathscr{Q}_{-}] = 1 \) , with \( \mathscr{P} \) and \( \mathscr{Q}_{-} \) \( 2{\times} 2 \) matrices of differential operators. These conditions on \( V_1 \) and \( V_2 \) yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints \( L_n \) (\( n\geq 0 \) ), where \( L_n \) annihilate the two modified-KdV \( \tau \) -functions whose product gives the partition function of the Unitary Matrix Model.
@article {key1181066m,
AUTHOR = {Anagnostopoulos, Konstantinos N. and
Bowick, Mark J. and Schwarz, Albert},
TITLE = {The solution space of the unitary matrix
model string equation and the {S}ato
{G}rassmannian},
JOURNAL = {Commun. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {148},
NUMBER = {3},
YEAR = {1992},
PAGES = {469--485},
DOI = {10.1007/BF02096545},
NOTE = {ArXiv:hep-th/9112066. MR:1181066. Zbl:0753.35073.},
ISSN = {0010-3616},
}
A. S. Schwarz and A. A. Tseytlin :
“Dilation shift under duality and torsion of elliptic complex ,”
Nuclear Phys. B
399 : 2–3
(July 1993 ),
pp. 691–708 .
MR
1226849
ArXiv
hep-th/9210015
article
Abstract
People
BibTeX
We observe that the ratio of determinants of 2d laplacians which appear in the duality transformation relating two sigma models with abelian isometries can be represented as a torsion of an elliptic (DeRham) complex. As a result, this ratio can be computed exactly and is given by the exponential of local functional of 2d metric and target space metric. In this way the well-known dilation shift under duality is reproduced. We also present the exact computation of the determinant which appears in the duality transformation in the path integral.
@article {key1226849m,
AUTHOR = {Schwarz, A. S. and Tseytlin, A. A.},
TITLE = {Dilation shift under duality and torsion
of elliptic complex},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {399},
NUMBER = {2--3},
MONTH = {July},
YEAR = {1993},
PAGES = {691--708},
DOI = {10.1016/0550-3213(93)90514-P},
NOTE = {ArXiv:hep-th/9210015. MR:1226849.},
ISSN = {0550-3213},
}
A. Schwarz :
“Geometry of Batalin–Vilkovisky quantization ,”
Commun. Math. Phys.
155 : 2
(1993 ),
pp. 249–260 .
MR
1230027
Zbl
0786.58017
ArXiv
hep-th/9205088
article
Abstract
BibTeX
The geometry of \( P \) -manifolds (odd symplectic manifolds) and \( SP \) -manifolds (\( P \) -manifolds provided with a volume element) is studied. A complete classification of these manifolds is given. This classification is used to prove some results about Batalin–Vilkovisky procedure of quantization, in particular to obtain a very general result about gauge independence of this procedure.
@article {key1230027m,
AUTHOR = {Schwarz, Albert},
TITLE = {Geometry of {B}atalin--{V}ilkovisky
quantization},
JOURNAL = {Commun. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {155},
NUMBER = {2},
YEAR = {1993},
PAGES = {249--260},
DOI = {10.1007/BF02097392},
NOTE = {ArXiv:hep-th/9205088. MR:1230027. Zbl:0786.58017.},
ISSN = {0010-3616},
}
A. Schwarz :
“Semiclassical approximation in Batalin–Vilkovisky formalism ,”
Commun. Math. Phys.
158 : 2
(1993 ),
pp. 373–396 .
MR
1249600
Zbl
0855.58005
ArXiv
hep-th/9210115
article
Abstract
BibTeX
The geometry of supermanifolds provided with a \( Q \) -structure (i.e. with an odd vector field \( Q \) satisfying \( \{Q,Q\} = 0 \) ), a \( P \) -structure (odd symplectic structure) and an \( S \) -structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin–Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion.
@article {key1249600m,
AUTHOR = {Schwarz, Albert},
TITLE = {Semiclassical approximation in {B}atalin--{V}ilkovisky
formalism},
JOURNAL = {Commun. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {158},
NUMBER = {2},
YEAR = {1993},
PAGES = {373--396},
DOI = {10.1007/BF02108080},
NOTE = {ArXiv:hep-th/9210115. MR:1249600. Zbl:0855.58005.},
ISSN = {0010-3616},
}
A. S. Schwarz :
Quantum field theory and topology .
Grundlehren der Mathematischen Wissenschaften 307 .
Springer (Berlin ),
1993 .
English translation of 1989 Russian original . A 1994 English-language monograph was partly based on this translation and the original.
MR
1276723
Zbl
0789.58004
book
BibTeX
@book {key1276723m,
AUTHOR = {Schwarz, Albert S.},
TITLE = {Quantum field theory and topology},
SERIES = {Grundlehren der Mathematischen Wissenschaften},
NUMBER = {307},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {viii + 274},
DOI = {10.1007/978-3-662-02943-5},
NOTE = {English translation of 1989 Russian
original. A 1994 English-language monograph
was partly based on this translation
and the original. MR:1276723. Zbl:0789.58004.},
ISSN = {0072-7830},
ISBN = {9783540547532},
}
A. Schwarz, M. Pohst, and F. Diaz y Diaz :
“A table of quintic number fields ,”
Math. Comput.
63 : 207
(1994 ),
pp. 361–376 .
MR
1219705
Zbl
0822.11087
article
Abstract
People
BibTeX
@article {key1219705m,
AUTHOR = {Schwarz, A. and Pohst, M. and Diaz y
Diaz, Francisco},
TITLE = {A table of quintic number fields},
JOURNAL = {Math. Comput.},
FJOURNAL = {Mathematics of Computation},
VOLUME = {63},
NUMBER = {207},
YEAR = {1994},
PAGES = {361--376},
DOI = {10.2307/2153581},
NOTE = {MR:1219705. Zbl:0822.11087.},
ISSN = {0025-5718},
}
A. Schwarz :
“Symmetry transformations in Batalin–Vilkovisky formalism ,”
Lett. Math. Phys.
31 : 4
(1994 ),
pp. 299–301 .
MR
1293493
Zbl
0802.58027
ArXiv
hep-th/9310124
article
Abstract
BibTeX
@article {key1293493m,
AUTHOR = {Schwarz, Albert},
TITLE = {Symmetry transformations in {B}atalin--{V}ilkovisky
formalism},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {31},
NUMBER = {4},
YEAR = {1994},
PAGES = {299--301},
DOI = {10.1007/BF00762792},
NOTE = {ArXiv:hep-th/9310124. MR:1293493. Zbl:0802.58027.},
ISSN = {0377-9017},
}
A. S. Schwarz :
Topology for physicists .
Grundlehren der Mathematischen Wissenschaften 308 .
Springer (Berlin ),
1994 .
Based on Kvantovaya teoriya polya i topologiya (1989) and its 1993 English translation .
MR
1301777
Zbl
0858.55001
book
BibTeX
@book {key1301777m,
AUTHOR = {Schwarz, Albert S.},
TITLE = {Topology for physicists},
SERIES = {Grundlehren der Mathematischen Wissenschaften},
NUMBER = {308},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1994},
PAGES = {xi + 296},
DOI = {10.1007/978-3-662-02998-5},
NOTE = {Based on \textit{Kvantovaya teoriya
polya i topologiya} (1989) and its 1993
English translation. MR:1301777. Zbl:0858.55001.},
ISSN = {0072-7830},
ISBN = {9783662029985},
}
M. Penkava and A. Schwarz :
“On some algebraic structures arising in string theory ,”
pp. 219–227
in
Perspectives in mathematical physics
(Taiwan, summer 1992 and Los Angeles, winter 1992 ).
Edited by R. C. Penner and S.-T. Yau .
Conference Proceedings and Lecture Notes in Geometry and Topology 3 .
International Press (Boston ),
1994 .
MR
1314668
Zbl
0871.17021
ArXiv
hep-th/9212072
incollection
Abstract
People
BibTeX
Lian and Zuckerman proved that the homology of a topological chiral algebra can be equipped with the structure of a BV-algebra; i.e., one can introduce a multiplication, an odd bracket, and an odd operator \( \Delta \) having the same properties as the corresponding operations in Batalin–Vilkovisky quantization procedure. We give a simple proof of their results and discuss a generalization of these results to the non chiral case. To simplify our proofs we use the following theorem giving a characterization of a BV-algebra in terms of multiplication and an operator \( \Delta \) : If \( \mathcal{A} \) is a supercommutative, associative algebra and \( \Delta \) is an odd second order derivation on \( \mathcal{A} \) satisfying \( \Delta^2 = 0 \) , one can provide \( \mathcal{A} \) with the structure of a BV-algebra.
@incollection {key1314668m,
AUTHOR = {Penkava, Michael and Schwarz, Albert},
TITLE = {On some algebraic structures arising
in string theory},
BOOKTITLE = {Perspectives in mathematical physics},
EDITOR = {Penner, Robert C. and Yau, Shing-Tung},
SERIES = {Conference Proceedings and Lecture Notes
in Geometry and Topology},
NUMBER = {3},
PUBLISHER = {International Press},
ADDRESS = {Boston},
YEAR = {1994},
PAGES = {219--227},
NOTE = {(Taiwan, summer 1992 and Los Angeles,
winter 1992). ArXiv:hep-th/9212072.
MR:1314668. Zbl:0871.17021.},
ISSN = {2644-0733},
ISBN = {9781571460097},
}
M. Atiyah, A. Borel, G. J. Chaitin, D. Friedan, J. Glimm, J. J. Gray, M. W. Hirsch, S. MacLane, B. B. Mandelbrot, D. Ruelle, A. Schwarz, K. Uhlenbeck, R. Thom, E. Witten, and C. Zeeman :
“Responses to ‘Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics’, by A. Jaffe and F. Quinn ,”
Bull. Am. Math. Soc., New Ser.
30 : 2
(April 1994 ),
pp. 178–207 .
Zbl
0803.01014
ArXiv
math/9404229
article
Abstract
People
BibTeX
@article {key0803.01014z,
AUTHOR = {Atiyah, Michael and Borel, Armand and
Chaitin, G. J. and Friedan, Daniel and
Glimm, James and Gray, Jeremy J. and
Hirsch, Morris W. and MacLane, Saunders
and Mandelbrot, Benoit B. and Ruelle,
David and Schwarz, Albert and Uhlenbeck,
Karen and Thom, Ren\'e and Witten, Edward
and Zeeman, Christopher},
TITLE = {Responses to ``Theoretical mathematics:
{T}oward a cultural synthesis of mathematics
and theoretical physics'', by {A}.~{J}affe
and {F}.~{Q}uinn},
JOURNAL = {Bull. Am. Math. Soc., New Ser.},
FJOURNAL = {Bulletin of the American Mathematical
Society. New Series},
VOLUME = {30},
NUMBER = {2},
MONTH = {April},
YEAR = {1994},
PAGES = {178--207},
DOI = {10.1090/S0273-0979-1994-00503-8},
NOTE = {ArXiv:math/9404229. Zbl:0803.01014.},
ISSN = {0273-0979},
}
D. Fuchs and A. Schwarz :
“Matrix Vieta theorem ,”
pp. 15–22
in
Lie groups and Lie algebras: E. B. Dynkin’s seminar .
Edited by S. G. Gindikin and E. B. Vinberg .
American Mathematical Society Translations. Series 2 169 .
American Mathematical Society (Providence, RI ),
1995 .
This book is also no. 26 in the Advances in Mathematics series.
MR
1364450
Zbl
0837.15011
ArXiv
math/9410207
incollection
Abstract
People
BibTeX
We consider generalizations of the Vieta formula (relating the coefficients of an algebraic equation to the roots) to the case of equations whose coefficients are order-\( k \) matrices.
Specifically, we prove that if \( X_1,\dots \) , \( X_n \) are solutions of an algebraic matrix equation
\[ X^n + A_1 X^{n-1} + \cdots + A_n = 0 ,\]
independent in the sense that they determine the coefficients \( A_1,\dots \) , \( A_n \) , then the trace of \( A_1 \) is the sum of the traces of the \( X_i \) , and the determinant of \( A_n \) is, up to a sign, the product of the determinants of the \( X_i \) . We generalize this to arbitrary rings with appropriate structures.
This result is related to and motivated by some constructions in non-commutative geometry.
@incollection {key1364450m,
AUTHOR = {Fuchs, Dmitry and Schwarz, Albert},
TITLE = {Matrix {V}ieta theorem},
BOOKTITLE = {Lie groups and {L}ie algebras: {E}.~{B}.
{D}ynkin's seminar},
EDITOR = {Gindikin, S. G. and Vinberg, E. B.},
SERIES = {American Mathematical Society Translations.
Series 2},
NUMBER = {169},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1995},
PAGES = {15--22},
NOTE = {This book is also no. 26 in the Advances
in Mathematics series. ArXiv:math/9410207.
MR:1364450. Zbl:0837.15011.},
ISSN = {0065-9290},
ISBN = {9780821804544},
}
M. Penkava and A. Schwarz :
“\( A_{\infty} \) algebras and the cohomology of moduli spaces ,”
pp. 91–107
in
Lie groups and Lie algebras: E. B. Dynkin’s seminar .
Edited by S. G. Gindikin and E. B. Vinberg .
American Mathematical Society Translations. Series 2 169 .
American Mathematical Society (Providence, RI ),
1995 .
This book is also no. 26 in the Advances in Mathematics series.
MR
1364455
Zbl
0863.17017
ArXiv
hep-th/9408064
incollection
Abstract
People
BibTeX
Let us consider an \( A_{\infty} \) algebra with an invariant inner product. The main goal of this paper is to classify the infinitesimal deformations of this \( A_{\infty} \) algebra preserving the inner product and to apply this result to the construction of homology classes on the moduli spaces of algebraic curves. With this aim, we define cyclic cohomology of an \( A_{\infty} \) algebra and show that it classifies the deformations we are interested in. To make the reading of our paper more independent of other works, we include a short review of Hochschild and cyclic cohomology of associative algebras, and explain the definition of \( A_{\infty} \) algebras.
@incollection {key1364455m,
AUTHOR = {Penkava, Michael and Schwarz, Albert},
TITLE = {\$A_{\infty}\$ algebras and the cohomology
of moduli spaces},
BOOKTITLE = {Lie groups and {L}ie algebras: {E}.~{B}.
{D}ynkin's seminar},
EDITOR = {Gindikin, S. G. and Vinberg, E. B.},
SERIES = {American Mathematical Society Translations.
Series 2},
NUMBER = {169},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1995},
PAGES = {91--107},
NOTE = {This book is also no. 26 in the Advances
in Mathematics series. ArXiv:hep-th/9408064.
MR:1364455. Zbl:0863.17017.},
ISSN = {0065-9290},
ISBN = {9780821804544},
}
A. Schwarz :
“Sigma-models having supermanifolds as target spaces ,”
Lett. Math. Phys.
38 : 1
(1996 ),
pp. 91–96 .
MR
1401058
Zbl
0859.58004
ArXiv
hep-th/9506070
article
Abstract
BibTeX
We study a topological sigma-model (\( A \) -model) in the case when the target space is an \( (m_0|m_1) \) -dimensional supermanifold. We prove under certain conditions that such a model is equivalent to an \( A \) -model having an \( (m_0 {-} m_1) \) -dimensional manifold as a target space. We use this result to prove that in the case when the target space of \( A \) -model is a complete intersection in a toric manifold, this \( A \) -model is equivalent to an \( A \) -model having a toric supermanifold as a target space.
@article {key1401058m,
AUTHOR = {Schwarz, Albert},
TITLE = {Sigma-models having supermanifolds as
target spaces},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {38},
NUMBER = {1},
YEAR = {1996},
PAGES = {91--96},
DOI = {10.1007/BF00398301},
NOTE = {ArXiv:hep-th/9506070. MR:1401058. Zbl:0859.58004.},
ISSN = {0377-9017},
}
A. Schwarz :
“Superanalogs of symplectic and contact geometry and their applications to quantum field theory ,”
pp. 203–218
in
Topics in statistical and theoretical physics: F. A. Berezin memorial volume .
Edited by R. L. Dobrushin, R. A. Minlos, M. A. Shubin, and A. M. Vershik .
American Mathematical Society Translations. Series 2 177 .
American Mathematical Society (Providence, RI ),
1996 .
This book is also no. 32 in the Advances in Mathematics series.
MR
1409176
Zbl
0873.58004
ArXiv
hep-th/9406120
incollection
Abstract
People
BibTeX
The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in quantum field theory. In particular, regarding \( N \) -superconformal geometry as particular case of contact complex geometry, one can better understand \( N = 2 \) superconformal field theory and its connection to topological conformal field theory. The odd symplectic geometry constitutes a mathematical basis of Batalin–Vilkovisky procedure of quantization of gauge theories. The exposition is based mostly on published papers. However, the paper contains also a review of some unpublished results (in the section devoted to the axiomatics of \( N = 2 \) superconformal theory and topological quantum field theory).
@incollection {key1409176m,
AUTHOR = {Schwarz, Albert},
TITLE = {Superanalogs of symplectic and contact
geometry and their applications to quantum
field theory},
BOOKTITLE = {Topics in statistical and theoretical
physics: {F}.~{A}. {B}erezin memorial
volume},
EDITOR = {Dobrushin, R. L. and Minlos, R. A. and
Shubin, M. A. and Vershik, A. M.},
SERIES = {American Mathematical Society Translations.
Series 2},
NUMBER = {177},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1996},
PAGES = {203--218},
NOTE = {This book is also no. 32 in the Advances
in Mathematics series. ArXiv:hep-th/9406120.
MR:1409176. Zbl:0873.58004.},
ISSN = {0065-9290},
ISBN = {9780821804254},
}
M. Alexandrov, A. Schwarz, O. Zaboronsky, and M. Kontsevich :
“The geometry of the master equation and topological quantum field theory ,”
Int. J. Mod. Phys. A
12 : 7
(1997 ),
pp. 1405–1429 .
MR
1432574
Zbl
1073.81655
ArXiv
hep-th/9502010
article
Abstract
People
BibTeX
In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation . Geometrically, such a solution can be considered as a \( QP \) -manifold, i.e. a supermanifold equipped with an odd vector field \( Q \) obeying \( \{Q,Q\} = 0 \) and with \( Q \) -invariant odd symplectic structure. We study geometry of \( QP \) -manifolds. In particular, we describe some construction of \( QP \) -manifolds and prove a classification theorem (under certain conditions).
We apply these geometric constructions to obtain in a natural way the action functionals of two-dimensional topological sigma-models and to show that the Chern–Simons theory in BV-formalism arises as a sigma-model with target space \( \Pi\mathcal{G} \) . (Here \( \mathcal{G} \) stands for a Lie algebra and \( \Pi \) denotes parity inversion.)
@article {key1432574m,
AUTHOR = {Alexandrov, M. and Schwarz, A. and Zaboronsky,
O. and Kontsevich, M.},
TITLE = {The geometry of the master equation
and topological quantum field theory},
JOURNAL = {Int. J. Mod. Phys. A},
FJOURNAL = {International Journal of Modern Physics
A},
VOLUME = {12},
NUMBER = {7},
YEAR = {1997},
PAGES = {1405--1429},
DOI = {10.1142/S0217751X97001031},
NOTE = {ArXiv:hep-th/9502010. MR:1432574. Zbl:1073.81655.},
ISSN = {0217-751X},
}
A. Connes and A. Schwarz :
“Matrix Vieta theorem revisited ,”
Lett. Math. Phys.
39 : 4
(1997 ),
pp. 349–353 .
MR
1449580
Zbl
0874.15010
article
Abstract
People
BibTeX
@article {key1449580m,
AUTHOR = {Connes, Alain and Schwarz, Albert},
TITLE = {Matrix {V}ieta theorem revisited},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {39},
NUMBER = {4},
YEAR = {1997},
PAGES = {349--353},
DOI = {10.1023/A:1007373114601},
NOTE = {MR:1449580. Zbl:0874.15010.},
ISSN = {0377-9017},
}
A. Schwarz and O. Zaboronsky :
“Supersymmetry and localization ,”
Commun. Math. Phys.
183 : 2
(1997 ),
pp. 463–476 .
MR
1461967
Zbl
0873.58003
ArXiv
hep-th/9511112
article
Abstract
People
BibTeX
@article {key1461967m,
AUTHOR = {Schwarz, Albert and Zaboronsky, Oleg},
TITLE = {Supersymmetry and localization},
JOURNAL = {Commun. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {183},
NUMBER = {2},
YEAR = {1997},
PAGES = {463--476},
DOI = {10.1007/BF02506415},
NOTE = {ArXiv:hep-th/9511112. MR:1461967. Zbl:0873.58003.},
ISSN = {0010-3616},
}
A. Konechny and A. Schwarz :
“Geometry of \( N = 1 \) super Yang–Mills theory in curved superspace ,”
J. Geom. Phys.
23 : 2
(1997 ),
pp. 97–110 .
MR
1467173
Zbl
0899.53061
ArXiv
hep-th/9609081
article
Abstract
People
BibTeX
Anatoly Vladimirovich Konechny
Related
@article {key1467173m,
AUTHOR = {Konechny, Anatoli and Schwarz, Albert},
TITLE = {Geometry of \$N = 1\$ super {Y}ang--{M}ills
theory in curved superspace},
JOURNAL = {J. Geom. Phys.},
FJOURNAL = {Journal of Geometry and Physics},
VOLUME = {23},
NUMBER = {2},
YEAR = {1997},
PAGES = {97--110},
DOI = {10.1016/S0393-0440(96)00050-2},
NOTE = {ArXiv:hep-th/9609081. MR:1467173. Zbl:0899.53061.},
ISSN = {0393-0440},
}
N. Nekrasov and A. Schwarz :
“Instantons on noncommutative \( \mathbb{R}^4 \) , and \( (2,0) \) superconformal six dimensional theory ,”
Commun. Math. Phys.
198 : 3
(1998 ),
pp. 689–703 .
MR
1670037
Zbl
0923.58062
ArXiv
hep-th/9802068
article
Abstract
People
BibTeX
We show that the resolution of moduli space of ideal instantons parameterizes the instantons on noncommutative \( \mathbb{R}^4 \) . This moduli space appears to be the Higgs branch of the theory of \( k \) \( D0 \) -branes bound to \( N \) \( D4 \) -branes by the expectation value of the \( B \) field. It also appears as a regularized version of the target space of supersymmetric quantum mechanics arising in the light cone description of \( (2,0) \) superconformal theories in six dimensions.
Nikita Alexandrovich Nekrasov
Related
@article {key1670037m,
AUTHOR = {Nekrasov, Nikita and Schwarz, Albert},
TITLE = {Instantons on noncommutative \$\mathbb{R}^4\$,
and \$(2,0)\$ superconformal six dimensional
theory},
JOURNAL = {Commun. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {198},
NUMBER = {3},
YEAR = {1998},
PAGES = {689--703},
DOI = {10.1007/s002200050490},
NOTE = {ArXiv:hep-th/9802068. MR:1670037. Zbl:0923.58062.},
ISSN = {0010-3616},
}
A. Connes, M. R. Douglas, and A. Schwarz :
“Noncommutative geometry and matrix theory: Compactification on tori ,”
J. High Energy Phys.
1998 : 2
(1998 ).
article no. 3, 35 pages.
MR
1613978
Zbl
1018.81052
ArXiv
hep-th/9711162
article
Abstract
People
BibTeX
We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory.
@article {key1613978m,
AUTHOR = {Connes, Alain and Douglas, Michael R.
and Schwarz, Albert},
TITLE = {Noncommutative geometry and matrix theory:
{C}ompactification on tori},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {1998},
NUMBER = {2},
YEAR = {1998},
DOI = {10.1088/1126-6708/1998/02/003},
NOTE = {article no. 3, 35 pages. ArXiv:hep-th/9711162.
MR:1613978. Zbl:1018.81052.},
ISSN = {1126-6708},
}
A. Schwarz :
“Symplectic formalism in conformal field theory ,”
pp. 957–977
in
Symétries quantiques / Quantum symmetries
(Les Houches, France, 1 August–8 September 1995 ).
Edited by A. Connes, K. Gaweedzki, and J. Zinn-Justin .
Elsevier (Amsterdam ),
1998 .
MR
1616364
Zbl
1050.81061
incollection
People
BibTeX
@incollection {key1616364m,
AUTHOR = {Schwarz, Albert},
TITLE = {Symplectic formalism in conformal field
theory},
BOOKTITLE = {Sym\'etries quantiques / {Q}uantum symmetries},
EDITOR = {Connes, Alain and Gaweedzki, Krzysztof
and Zinn-Justin, Jean},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {1998},
PAGES = {957--977},
NOTE = {(Les Houches, France, 1 August--8 September
1995). MR:1616364. Zbl:1050.81061.},
ISSN = {9780444828675},
}
A. Schwarz :
“Grassmann and string theory ,”
Commun. Math. Phys.
199 : 1
(1998 ),
pp. 1–24 .
MR
1660223
Zbl
0921.58078
ArXiv
hep-th/9610122
article
Abstract
BibTeX
The infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of the Grassmannian. We present new facts supporting this hypothesis. In particular, it is shown that Grassmannians can be considered as generalized moduli spaces; this statement permits us to define corresponding “string amplitudes” (at least formally). One can conjecture that it is possible to explain the relation between non-perturbative and perturbative string theory by means of localization theorems for equivariant cohomology; this conjecture is based on the characterization of moduli spaces, relevant to string theory, as sets consisting of points with large stabilizers in certain groups acting on the Grassmannian. We describe an involution on the Grassmannian that could be related to \( S \) -duality in string theory.
@article {key1660223m,
AUTHOR = {Schwarz, Albert},
TITLE = {Grassmann and string theory},
JOURNAL = {Commun. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {199},
NUMBER = {1},
YEAR = {1998},
PAGES = {1--24},
DOI = {10.1007/s002200050493},
NOTE = {ArXiv:hep-th/9610122. MR:1660223. Zbl:0921.58078.},
ISSN = {0010-3616},
}
A. Schwarz :
“Morita equivalence and duality ,”
Nucl. Phys., B
534 : 3
(1998 ),
pp. 720–738 .
MR
1663471
Zbl
1079.81066
ArXiv
hep-th/9805034
article
Abstract
BibTeX
It was shown by Connes, Douglas, Schwarz [hep-th/9711162] that one can compactify M(atrix) theory on a non-commutative torus \( T_{\theta} \) . We prove that compactifications on Morita equivalent tori are in some sense physically equivalent. This statement can be considered as a generalization of non-classical \( SL(2\mathbb{Z})_N \) duality conjectured by Connes, Douglas and Schwarz for compactifications on two-dimensional non-commutative tori.
@article {key1663471m,
AUTHOR = {Schwarz, Albert},
TITLE = {Morita equivalence and duality},
JOURNAL = {Nucl. Phys., B},
FJOURNAL = {Nuclear Physics. B},
VOLUME = {534},
NUMBER = {3},
YEAR = {1998},
PAGES = {720--738},
DOI = {10.1016/S0550-3213(98)00550-1},
NOTE = {ArXiv:hep-th/9805034. MR:1663471. Zbl:1079.81066.},
ISSN = {0550-3213},
}
A. Konechny and A. Schwarz :
“On \( (k\oplus l|g) \) -dimensional supermanifolds ,”
pp. 201–206
in
Supersymmetry and quantum field theory
(Kharkov, Ukraine, 5–7 January 1997 ).
Edited by J. Wess and V. P. Akulov .
Lecture Notes in Physics 509 .
1998 .
Proceedings of the D. Volkov Memorial Seminar.
MR
1677320
Zbl
0937.58001
incollection
Abstract
People
BibTeX
@incollection {key0937.58001z,
AUTHOR = {Konechny, A. and Schwarz, A.},
TITLE = {On \$(k\oplus l|g)\$-dimensional supermanifolds},
BOOKTITLE = {Supersymmetry and quantum field theory},
EDITOR = {Wess, Julius and Akulov, Vladimir P.},
SERIES = {Lecture Notes in Physics},
NUMBER = {509},
YEAR = {1998},
PAGES = {201--206},
NOTE = {(Kharkov, Ukraine, 5--7 January 1997).
Proceedings of the D. Volkov Memorial
Seminar. Zbl:0937.58001.},
ISSN = {0075-8450},
ISBN = {9783540646235},
}
L. Friedlander and A. Schwarz :
“Grassmannian and elliptic operators ,”
pp. 79–88
in
Higher homotopy structures in topology and mathematical physics
(Poughkeepsie, NY, 13–15 June 1996 ).
Edited by J. McCleary .
Contemporary Mathematics 227 .
1999 .
Conference to honor the 60th birthday of Jim Stasheff.
MR
1665462
Zbl
0923.58053
ArXiv
funct-an/9704003
incollection
Abstract
People
BibTeX
@incollection {key1665462m,
AUTHOR = {Friedlander, Leonid and Schwarz, Albert},
TITLE = {Grassmannian and elliptic operators},
BOOKTITLE = {Higher homotopy structures in topology
and mathematical physics},
EDITOR = {McCleary, John},
SERIES = {Contemporary Mathematics},
NUMBER = {227},
YEAR = {1999},
PAGES = {79--88},
NOTE = {(Poughkeepsie, NY, 13--15 June 1996).
Conference to honor the 60th birthday
of Jim Stasheff. ArXiv:funct-an/9704003.
MR:1665462. Zbl:0923.58053.},
ISSN = {0271-4132},
ISBN = {9780821809136},
}
M. A. Rieffel and A. Schwarz :
“Morita equivalence of multidimensional noncommutative tori ,”
Int. J. Math.
10 : 2
(1999 ),
pp. 289–299 .
MR
1687145
Zbl
0968.46060
ArXiv
math/9803057
article
Abstract
People
BibTeX
One can describe an \( n \) -dimensional noncommutative torus by means of an antisymmetric \( n{\times} n \) matrix \( \theta \) . We construct an action of the group \( SO(n,n|\mathbb{Z}) \) on the space of \( n{\times} n \) antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched.
@article {key1687145m,
AUTHOR = {Rieffel, Marc A. and Schwarz, Albert},
TITLE = {Morita equivalence of multidimensional
noncommutative tori},
JOURNAL = {Int. J. Math.},
FJOURNAL = {International Journal of Mathematics},
VOLUME = {10},
NUMBER = {2},
YEAR = {1999},
PAGES = {289--299},
DOI = {10.1142/S0129167X99000100},
NOTE = {ArXiv:math/9803057. MR:1687145. Zbl:0968.46060.},
ISSN = {0129-167X},
}
A. Konechny and A. Schwarz :
“Supersymmetry algebra and BPS states of super Yang–Mills theories on noncommutative tori ,”
Phys. Lett., B
453 : 1–2
(1999 ),
pp. 23–29 .
MR
1690319
Zbl
1058.58500
ArXiv
hep-th/9901077
article
Abstract
People
BibTeX
We consider 10-dimensional super Yang–Mills theory with topological terms compactified on a noncommutative torus. We calculate supersymmetry algebra and derive BPS energy spectra from it. The cases of \( d \) -dimensional tori with \( d = 2,\,3,\,4 \) are considered in full detail. \( SO(d,d,\mathbb{Z}) \) -invariance of the BPS spectrum and relation of new results to the previous work in this direction are discussed.
Anatoly Vladimirovich Konechny
Related
@article {key1690319m,
AUTHOR = {Konechny, Anatoly and Schwarz, Albert},
TITLE = {Supersymmetry algebra and {BPS} states
of super {Y}ang--{M}ills theories on
noncommutative tori},
JOURNAL = {Phys. Lett., B},
FJOURNAL = {Physics Letters. B},
VOLUME = {453},
NUMBER = {1--2},
YEAR = {1999},
PAGES = {23--29},
DOI = {10.1016/S0370-2693(99)00335-4},
NOTE = {ArXiv:hep-th/9901077. MR:1690319. Zbl:1058.58500.},
ISSN = {0370-2693},
}
A. Konechny and A. Schwarz :
“BPS states on non-commutative tori and duality ,”
Nucl. Phys., B
550 : 3
(1999 ),
pp. 561–584 .
MR
1693262
Zbl
0949.58004
ArXiv
hep-th/9811159
article
Abstract
People
BibTeX
We study gauge theories on non-commutative tori. It has been proved that Morita equivalence of non-commutative tori leads to a physical equivalence (\( SO(d,d|\mathbb{Z}) \) -duality) of the corresponding gauge theories [Nucl. Phys. B 534 (1998) 720]. We calculate the energy spectrum of maximally supersymmetric BPS states in these theories and show that this spectrum agrees with the . The relation of our results with those of recent calculations is discussed.
Anatoly Vladimirovich Konechny
Related
@article {key1693262m,
AUTHOR = {Konechny, Anatoly and Schwarz, Albert},
TITLE = {{BPS} states on non-commutative tori
and duality},
JOURNAL = {Nucl. Phys., B},
FJOURNAL = {Nuclear Physics. B},
VOLUME = {550},
NUMBER = {3},
YEAR = {1999},
PAGES = {561--584},
DOI = {10.1016/S0550-3213(99)00184-4},
NOTE = {ArXiv:hep-th/9811159. MR:1693262. Zbl:0949.58004.},
ISSN = {0550-3213},
}
S. P. Novikov and A. S. Shvarts :
“Discrete Lagrangian systems on graphs: Symplecto-topological properties ,”
Uspekhi Mat. Nauk
54 : 1(325)
(1999 ),
pp. 257–258 .
An English translation was published in Russ. Math. Surv. 54 :1 (1999) .
MR
1706803
ArXiv
math-ph/0004011
article
People
BibTeX
@article {key1706803m,
AUTHOR = {Novikov, S. P. and Shvarts, A. S.},
TITLE = {Discrete {L}agrangian systems on graphs:
{S}ymplecto-topological properties},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk. Akademiya
Nauk SSSR i Moskovskoe Matematicheskoe
Obshchestvo},
VOLUME = {54},
NUMBER = {1(325)},
YEAR = {1999},
PAGES = {257--258},
DOI = {10.4213/rm126},
NOTE = {An English translation was published
in \textit{Russ. Math. Surv.} \textbf{54}:1
(1999). ArXiv:math-ph/0004011. MR:1706803.},
ISSN = {0042-1316},
}
B. Pioline and A. Schwarz :
“Morita equivalence and \( T \) -duality (or \( B \) versus \( \Theta \) ) ,”
J. High Energy Phys.
1999 : 8
(1999 ).
article no. 21, 16 pages.
MR
1715542
Zbl
1060.81612
ArXiv
hep-th/9908019
article
Abstract
People
BibTeX
\( T \) -duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang–Mills theory on a non-commutative torus (NCSYM). Even though the two have the same structure group, they differ in their action since Morita equivalence makes crucial use of an additional modulus on the NCSYM side, the constant abelian magnetic background. In this paper, we reanalyze and clarify the correspondence between M(atrix) theory and NCSYM, and provide two resolutions of this puzzle. In the first of them, the standard map is kept and the extra modulus is ignored, but the anomalous transformation is offset by the M(atrix) theory “rest term”. In the second, the standard map is modified so that the duality transformations agree, and a \( SO(d) \) symmetry is found to eliminate the spurious modulus. We argue that this is a true symmetry of supersymmetric Born–Infeld theory on a non-commutative torus, which allows to freely trade a constant magnetic background for non-commutativity of the base-space. We also obtain a BPS mass formula for this theory, invariant under \( T \) -duality, \( U \) -duality, and continuous \( SO(d) \) symmetry.
@article {key1715542m,
AUTHOR = {Pioline, Boris and Schwarz, Albert},
TITLE = {Morita equivalence and \$T\$-duality (or
\$B\$ versus \$\Theta\$)},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {1999},
NUMBER = {8},
YEAR = {1999},
DOI = {10.1088/1126-6708/1999/08/021},
NOTE = {article no. 21, 16 pages. ArXiv:hep-th/9908019.
MR:1715542. Zbl:1060.81612.},
ISSN = {1126-6708},
}
A. Konechny and A. Schwarz :
“\( 1/4 \) -BPS states on noncommutative tori ,”
J. High Energy Phys.
1999 : 9
(1999 ).
article no. 30, 15 pages.
MR
1720696
Zbl
0957.81086
ArXiv
hep-th/9907008
article
Abstract
People
BibTeX
Anatoly Vladimirovich Konechny
Related
@article {key1720696m,
AUTHOR = {Konechny, Anatoly and Schwarz, Albert},
TITLE = {\$1/4\$-{BPS} states on noncommutative
tori},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {1999},
NUMBER = {9},
YEAR = {1999},
DOI = {10.1088/1126-6708/1999/09/030},
NOTE = {article no. 30, 15 pages. ArXiv:hep-th/9907008.
MR:1720696. Zbl:0957.81086.},
ISSN = {1126-6708},
}
A. Schwarz :
“Quantum observables, Lie algebra homology and TQFT ,”
Lett. Math. Phys.
49 : 2
(1999 ),
pp. 115–122 .
MR
1728307
Zbl
1029.81064
ArXiv
hep-th/9904168
article
Abstract
BibTeX
@article {key1728307m,
AUTHOR = {Schwarz, Albert},
TITLE = {Quantum observables, {L}ie algebra homology
and {TQFT}},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {49},
NUMBER = {2},
YEAR = {1999},
PAGES = {115--122},
DOI = {10.1023/A:1007684424728},
NOTE = {ArXiv:hep-th/9904168. MR:1728307. Zbl:1029.81064.},
ISSN = {0377-9017},
}
A. Schwarz, A. Sossinsky, C. Roger, B. Feigin, S. Tabachnikov, and A. Astashkevich :
“Appendix: Personal notes ,”
pp. 301–313
in
Differential topology, infinite-dimensional Lie algebras, and applications: D. B. Fuchs’ 60th anniversary collection .
Edited by A. Astashkevich and S. Tabachnikov .
American Mathematical Society Translations. Series 2 194 .
American Mathematical Society (Providence, RI ),
1999 .
This book is also no. 44 in the “Advances in Mathematics” series.
MR
1729370
Zbl
0960.01012
incollection
People
BibTeX
@incollection {key1729370m,
AUTHOR = {Schwarz, Albert and Sossinsky, Alexei
and Roger, Claude and Feigin, Boris
and Tabachnikov, Sergei and Astashkevich,
Alexander},
TITLE = {Appendix: {P}ersonal notes},
BOOKTITLE = {Differential topology, infinite-dimensional
{L}ie algebras, and applications: {D}.~{B}.
{F}uchs' 60th anniversary collection},
EDITOR = {Astashkevich, Alexander and Tabachnikov,
Serge},
SERIES = {American Mathematical Society Translations.
Series 2},
NUMBER = {194},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1999},
PAGES = {301--313},
NOTE = {This book is also no. 44 in the ``Advances
in Mathematics'' series. MR:1729370.
Zbl:0960.01012.},
ISSN = {0065-9290},
ISBN = {9780821820322},
}
A. Schwarz :
“Noncommutative supergeometry and duality ,”
Lett. Math. Phys.
50 : 4
(1999 ),
pp. 309–321 .
MR
1768707
Zbl
0967.58004
ArXiv
hep-th/9912212
article
Abstract
BibTeX
We introduce a notion of \( \mathcal{Q} \) -algebra that can be considered as a generalization of the notion of \( \mathcal{Q} \) -manifold (a supermanifold equipped with an odd vector field obeying \( \{\mathcal{Q},\mathcal{Q}\} = 0 \) ). We develop the theory of connections on modules over \( \mathcal{Q} \) -algebras and prove a general duality theorem for gauge theories on such modules. This theorem contains as a simplest case \( SO(d,d,\mathbb{Z}) \) -duality of gauge theories on noncommutative tori.
@article {key1768707m,
AUTHOR = {Schwarz, Albert},
TITLE = {Noncommutative supergeometry and duality},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {50},
NUMBER = {4},
YEAR = {1999},
PAGES = {309--321},
DOI = {10.1023/A:1007621011698},
NOTE = {ArXiv:hep-th/9912212. MR:1768707. Zbl:0967.58004.},
ISSN = {0377-9017},
}
S. P. Novikov and A. S. Shvarts :
“Discrete Lagrangian systems on graphs: Symplecto-topological properties ,”
Russ. Math. Surv.
54 : 1
(February 1999 ),
pp. 258–259 .
English translation of Russian original published in Uspekhi Mat. Nauk 54 :1(325) (1999) .
Zbl
0952.37011
article
Abstract
People
BibTeX
This paper continues [Novikov 1997, 1999, 1998], where the construction of a symplectic “Wronskian” was developed for linear systems on graphs and applied in scattering theory for graphs with tails.
@article {key0952.37011z,
AUTHOR = {Novikov, S. P. and Shvarts, A. S.},
TITLE = {Discrete {L}agrangian systems on graphs:
{S}ymplecto-topological properties},
JOURNAL = {Russ. Math. Surv.},
FJOURNAL = {Russian Mathematical Surveys},
VOLUME = {54},
NUMBER = {1},
MONTH = {February},
YEAR = {1999},
PAGES = {258--259},
DOI = {10.1070/RM1999v054n01ABEH000126},
NOTE = {English translation of Russian original
published in \textit{Uspekhi Mat. Nauk}
\textbf{54}:1(325) (1999). Zbl:0952.37011.},
ISSN = {0036-0279},
}
A. Astashkevich, N. Nekrasov, and A. Schwarz :
“On noncommutative Nahm transform ,”
Comm. Math. Phys.
211 : 1
(2000 ),
pp. 167–182 .
MR
1757011
Zbl
1024.81046
ArXiv
hep-th/9810147
article
Abstract
People
BibTeX
Nikita Alexandrovich Nekrasov
Related
Alexander B. Astashkevich
Related
@article {key1757011m,
AUTHOR = {Astashkevich, Alexander and Nekrasov,
Nikita and Schwarz, Albert},
TITLE = {On noncommutative {N}ahm transform},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {211},
NUMBER = {1},
YEAR = {2000},
PAGES = {167--182},
DOI = {10.1007/s002200050807},
NOTE = {ArXiv:hep-th/9810147. MR:1757011. Zbl:1024.81046.},
ISSN = {0010-3616},
}
A. Schwarz :
“Noncommutative algebraic equations and the noncommutative eigenvalue problem ,”
Lett. Math. Phys.
52 : 2
(2000 ),
pp. 177–184 .
MR
1786861
Zbl
0972.15001
ArXiv
hep-th/0004088
article
Abstract
BibTeX
We analyze the perturbation series for the noncommutative eigenvalue problem \( AX = X\lambda \) , where \( \lambda \) is an element of a noncommutative ring, \( A \) is a matrix, and \( X \) is a column vector with entries from this ring. As a corollary, we obtain a theorem about the structure of perturbation series for \( \operatorname{Tr}x^r \) where \( x \) is a solution of a noncommutative algebraic equation (for \( r = 1 \) this theorem was proved by Aschieri, Brace, Morariu, and Zumino (hep-th/0003228), and used to study the Born–Infeld Lagrangian for the gauge group \( U(1)^k \) ).
@article {key1786861m,
AUTHOR = {Schwarz, Albert},
TITLE = {Noncommutative algebraic equations and
the noncommutative eigenvalue problem},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {52},
NUMBER = {2},
YEAR = {2000},
PAGES = {177--184},
DOI = {10.1023/A:1007624505615},
NOTE = {ArXiv:hep-th/0004088. MR:1786861. Zbl:0972.15001.},
ISSN = {0377-9017},
}
A. Konechny and A. Schwarz :
“Moduli spaces of maximally supersymmetric solutions on non-commutative tori and non-commutative orbifolds ,”
J. High Energy Phys.
2000 : 9
(2000 ),
pp. article no. 005, 24 pages .
MR
1789106
Zbl
0989.81623
ArXiv
hep-th/0005174
article
Abstract
People
BibTeX
Anatoly Vladimirovich Konechny
Related
@article {key1789106m,
AUTHOR = {Konechny, Anatoly and Schwarz, Albert},
TITLE = {Moduli spaces of maximally supersymmetric
solutions on non-commutative tori and
non-commutative orbifolds},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {2000},
NUMBER = {9},
YEAR = {2000},
PAGES = {article no. 005, 24 pages},
DOI = {10.1088/1126-6708/2000/09/005},
NOTE = {ArXiv:hep-th/0005174. MR:1789106. Zbl:0989.81623.},
ISSN = {1126-6708},
}
A. Konechny and A. Schwarz :
“Compactification of M(atrix) theory on noncommutative toroidal orbifolds ,”
Nuclear Phys. B
591 : 3
(2000 ),
pp. 667–684 .
MR
1797572
Zbl
1042.81580
ArXiv
hep-th/9912185
article
Abstract
People
BibTeX
It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori arise naturally in consideration of toroidal compactifications of M(atrix) theory. A similar analysis of toroidal \( \mathbb{Z}_2 \) orbifolds leads to the algebra \( B_{\theta} \) that can be defined as a crossed product of noncommutative torus and the group \( \mathbb{Z}_2 \) . Our paper is devoted to the study of projective modules over \( B_{\theta} \) (\( \mathbb{Z}_2 \) -equivariant projective modules over a noncommutative torus). We analyze the Morita equivalence (duality) for \( B_{\theta} \) algebras working out the two-dimensional case in detail.
Anatoly Vladimirovich Konechny
Related
@article {key1797572m,
AUTHOR = {Konechny, Anatoly and Schwarz, Albert},
TITLE = {Compactification of {M}(atrix) theory
on noncommutative toroidal orbifolds},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {591},
NUMBER = {3},
YEAR = {2000},
PAGES = {667--684},
DOI = {10.1016/S0550-3213(00)00544-7},
NOTE = {ArXiv:hep-th/9912185. MR:1797572. Zbl:1042.81580.},
ISSN = {0550-3213},
}
A. Konechny and A. Schwarz :
“Theory of \( (k\oplus l|q) \) -dimensional supermanifolds ,”
Selecta Math. (N.S.)
6 : 4
(2000 ),
pp. 471–486 .
MR
1847384
Zbl
1001.58001
article
Abstract
People
BibTeX
Anatoly Vladimirovich Konechny
Related
@article {key1847384m,
AUTHOR = {Konechny, Anatoly and Schwarz, Albert},
TITLE = {Theory of \$(k\oplus l|q)\$-dimensional
supermanifolds},
JOURNAL = {Selecta Math. (N.S.)},
FJOURNAL = {Selecta Mathematica. New Series},
VOLUME = {6},
NUMBER = {4},
YEAR = {2000},
PAGES = {471--486},
DOI = {10.1007/PL00001396},
NOTE = {MR:1847384. Zbl:1001.58001.},
ISSN = {1022-1824},
}
A. Schwarz :
“Noncommutative instantons: A new approach ,”
Comm. Math. Phys.
221 : 2
(2001 ),
pp. 433–450 .
MR
1845331
Zbl
0989.46040
ArXiv
hep-th/0102182
article
Abstract
BibTeX
We discuss instantons on noncommutative four-dimensional Euclidean space. In the commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field at infinity. However, technically it is more convenient to work on the four-dimensional sphere. We will show that the situation in the noncommutative case is quite similar. One can analyze instantons taking as a starting point the algebra of smooth functions vanishing at infinity, but it is convenient to add a unit element to this algebra (this corresponds to a transition to a sphere at the level of topology). Our approach is more rigorous than previous considerations; it seems that it is also simpler and more transparent. In particular, we obtain the ADHM equations in a very simple way.
@article {key1845331m,
AUTHOR = {Schwarz, Albert},
TITLE = {Noncommutative instantons: {A} new approach},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {221},
NUMBER = {2},
YEAR = {2001},
PAGES = {433--450},
DOI = {10.1007/s002200100481},
NOTE = {ArXiv:hep-th/0102182. MR:1845331. Zbl:0989.46040.},
ISSN = {0010-3616},
}
A. Schwarz :
“Theta functions on noncommutative tori ,”
Lett. Math. Phys.
58 : 1
(2001 ),
pp. 81–90 .
MR
1865115
Zbl
1032.53082
ArXiv
math/0107186
article
Abstract
BibTeX
Ordinary theta functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta functions as holomorphic elements of projective modules over noncommutative tori (theta vectors). The theory of these new objects is not only more general, but also much simpler than the theory of ordinary theta-functions. It seems that the theory of theta vectors should be closely related to Manin’s theory of quantized theta functions, but we don’t analyze this relation.
@article {key1865115m,
AUTHOR = {Schwarz, Albert},
TITLE = {Theta functions on noncommutative tori},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {58},
NUMBER = {1},
YEAR = {2001},
PAGES = {81--90},
DOI = {10.1023/A:1012515417396},
NOTE = {ArXiv:math/0107186. MR:1865115. Zbl:1032.53082.},
ISSN = {0377-9017},
}
A. Schwarz :
“Topological quantum field theories ,”
pp. 123–142
in
XIIIth International Congress on Mathematical Physics
(London, 17–22 July 2000 ).
Edited by A. Grigoryan, A. Fokas, T. Kibble, and B. Zegarlinski .
International Press (Boston ),
2001 .
MR
1883299
Zbl
1043.81066
ArXiv
hep-th/0011260
incollection
People
BibTeX
@incollection {key1883299m,
AUTHOR = {Schwarz, Albert},
TITLE = {Topological quantum field theories},
BOOKTITLE = {X{III}th {I}nternational {C}ongress
on {M}athematical {P}hysics},
EDITOR = {Grigoryan, A. and Fokas, A. and Kibble,
T. and Zegarlinski, B.},
PUBLISHER = {International Press},
ADDRESS = {Boston},
YEAR = {2001},
PAGES = {123--142},
NOTE = {(London, 17--22 July 2000). ArXiv:hep-th/0011260.
MR:1883299. Zbl:1043.81066.},
ISBN = {9781571460851},
}
A. Schwarz :
“Gauge theories on noncommutative spaces ,”
pp. 461–466
in
XIIIth International Congress on Mathematical Physics
(London, 17–22 July 2000 ).
Edited by A. Grigoryan, A. Fokas, T. Kibble, and B. Zegarlinski .
International Press (Boston ),
2001 .
MR
1883340
Zbl
1031.81064
ArXiv
hep-th/0011261
incollection
People
BibTeX
@incollection {key1883340m,
AUTHOR = {Schwarz, Albert},
TITLE = {Gauge theories on noncommutative spaces},
BOOKTITLE = {X{III}th {I}nternational {C}ongress
on {M}athematical {P}hysics},
EDITOR = {Grigoryan, A. and Fokas, A. and Kibble,
T. and Zegarlinski, B.},
PUBLISHER = {International Press},
ADDRESS = {Boston},
YEAR = {2001},
PAGES = {461--466},
NOTE = {(London, 17--22 July 2000). ArXiv:hep-th/0011261.
MR:1883340. Zbl:1031.81064.},
ISBN = {9781571460851},
}
A. Astashkevich and A. Schwarz :
“Projective modules over non-commutative tori: Classification of modules with constant curvature connection ,”
J. Oper. Theory
46 : 3 (supplement)
(2001 ),
pp. 619–634 .
Dedicated to Professor D. B. Fuchs on his 60th birthday.
MR
1897158
Zbl
0996.46031
ArXiv
math/9904139
article
Abstract
People
BibTeX
We study finitely generated projective modules over noncommutative tori. We prove that for every module \( E \) with constant curvature connection the corresponding element \( [E] \) of the K-group is a generalized quadratic exponent and, conversely, for every positive generalized quadratic exponent \( \mu \) in the K-group one can find such a module \( E \) with constant curvature connection that \( [E] = \mu \) . In physical words we give necessary and sufficient conditions for existence of \( 1/2 \) BPS states in terms of topological numbers.
@article {key1897158m,
AUTHOR = {Astashkevich, Alexander and Schwarz,
Albert},
TITLE = {Projective modules over non-commutative
tori: {C}lassification of modules with
constant curvature connection},
JOURNAL = {J. Oper. Theory},
FJOURNAL = {Journal of Operator Theory},
VOLUME = {46},
NUMBER = {3 (supplement)},
YEAR = {2001},
PAGES = {619--634},
NOTE = {Dedicated to Professor D. B. Fuchs on
his 60th birthday. ArXiv:math/9904139.
MR:1897158. Zbl:0996.46031.},
ISSN = {0379-4024},
}
A. Konechny and A. Schwarz :
“Introduction to M(atrix) theory and noncommutative geometry ,”
Phys. Rep.
360 : 5–6
(2002 ),
pp. 353–465 .
MR
1892926
Zbl
0985.81126
ArXiv
hep-th/0012145
article
Abstract
People
BibTeX
Noncommutative geometry is based on an idea that an associative algebra can be regarded as “an algebra of functions on a noncommutative space”. The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang–Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was found recently that Yang–Mills theories on noncommutative spaces appear naturally in string/M-theory; the notions and results of noncommutative geometry were applied very successfully to the problems of physics.
In this paper we give a mostly self-contained review of some aspects of M(atrix) theory, of Connes’ noncommutative geometry and of applications of noncommutative geometry to M(atrix) theory. The topics include introduction to BFSS and IKKT matrix models, compactifications on noncommutative tori, a review of basic notions of noncommutative geometry with a detailed discussion of noncommutative tori, Morita equivalence and \( SO(d,d|\mathbb{Z}) \) -duality, an elementary discussion of noncommutative orbifolds, noncommutative solitons and instantons. The review is primarily intended for physicists who would like to learn some basic techniques of noncommutative geometry and how they can be applied in string theory and to mathematicians who would like to learn about some new problems arising in theoretical physics.
The second part of the review devoted to solitons and instantons on noncommutative Euclidean space is almost independent of the first part.
Anatoly Vladimirovich Konechny
Related
@article {key1892926m,
AUTHOR = {Konechny, Anatoly and Schwarz, Albert},
TITLE = {Introduction to {M}(atrix) theory and
noncommutative geometry},
JOURNAL = {Phys. Rep.},
FJOURNAL = {Physics Reports. A Review Section of
Physics Letters},
VOLUME = {360},
NUMBER = {5--6},
YEAR = {2002},
PAGES = {353--465},
DOI = {10.1016/S0370-1573(01)00096-5},
NOTE = {ArXiv:hep-th/0012145. MR:1892926. Zbl:0985.81126.},
ISSN = {0370-1573},
}
M. Dieng and A. Schwarz :
“Differential and complex geometry of two-dimensional noncommutative tori ,”
Lett. Math. Phys.
61 : 3
(2002 ),
pp. 263–270 .
MR
1942364
Zbl
1019.58004
ArXiv
math/0203160
article
Abstract
People
BibTeX
@article {key1942364m,
AUTHOR = {Dieng, Momar and Schwarz, Albert},
TITLE = {Differential and complex geometry of
two-dimensional noncommutative tori},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {61},
NUMBER = {3},
YEAR = {2002},
PAGES = {263--270},
DOI = {10.1023/A:1021272314232},
NOTE = {ArXiv:math/0203160. MR:1942364. Zbl:1019.58004.},
ISSN = {0377-9017},
}
A. Schwarz :
“Gauge theories on noncommutative Euclidean spaces ,”
pp. 794–803
in
Multiple facets of quantization and supersymmetry: Michael Marinov memorial volume .
Edited by M. Olshanetsky and A. Vainshtein .
World Scientific (River Edge, NJ ),
2002 .
MR
1964925
Zbl
1026.81062
ArXiv
hep-th/0111174
incollection
Abstract
People
BibTeX
@incollection {key1964925m,
AUTHOR = {Schwarz, Albert},
TITLE = {Gauge theories on noncommutative {E}uclidean
spaces},
BOOKTITLE = {Multiple facets of quantization and
supersymmetry: {M}ichael {M}arinov memorial
volume},
EDITOR = {Olshanetsky, Mikhail and Vainshtein,
Arkady},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {2002},
PAGES = {794--803},
DOI = {10.1142/9789812777065_0042},
NOTE = {ArXiv:hep-th/0111174. MR:1964925. Zbl:1026.81062.},
ISBN = {9789814488112},
}
A. Schwarz :
“Noncommutative supergeometry, duality and deformations ,”
Nuclear Phys. B
650 : 3
(2003 ),
pp. 475–496 .
To Alain Connes on his 55th birthday.
MR
1952770
Zbl
1006.81083
ArXiv
hep-th/0210271
article
Abstract
People
BibTeX
Following Lett. Math. Phys. 50 (1999) 309, we introduce a notion of \( \mathcal{Q} \) -algebra that can be considered as a generalization of the notion of \( \mathcal{Q} \) -manifold (a supermanifold equipped with an odd vector field obeying \( \{Q,Q\} = 0 \) ). We develop the theory of connections on modules over \( \mathcal{Q} \) -algebras and prove a general duality theorem for gauge theories on such modules. This theorem containing as a simplest case \( SO(d,d,\mathbb{Z}) \) -duality of gauge theories on noncommutative tori can be applied also in more complicated situations. We show that \( \mathcal{Q} \) -algebras appear naturally in Fedosov construction of formal deformation of commutative algebras of functions and that similar \( \mathcal{Q} \) -algebras can be constructed also in the case when the deformation parameter is not formal.
@article {key1952770m,
AUTHOR = {Schwarz, Albert},
TITLE = {Noncommutative supergeometry, duality
and deformations},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {650},
NUMBER = {3},
YEAR = {2003},
PAGES = {475--496},
DOI = {10.1016/S0550-3213(02)01088-X},
NOTE = {To Alain Connes on his 55th birthday.
ArXiv:hep-th/0210271. MR:1952770. Zbl:1006.81083.},
ISSN = {0550-3213},
}
A. Polishchuk and A. Schwarz :
“Categories of holomorphic vector bundles on noncommutative two-tori ,”
Comm. Math. Phys.
236 : 1
(2003 ),
pp. 135–159 .
MR
1977884
Zbl
1033.58009
ArXiv
math/0211262
article
Abstract
People
BibTeX
@article {key1977884m,
AUTHOR = {Polishchuk, A. and Schwarz, A.},
TITLE = {Categories of holomorphic vector bundles
on noncommutative two-tori},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {236},
NUMBER = {1},
YEAR = {2003},
PAGES = {135--159},
DOI = {10.1007/s00220-003-0813-9},
NOTE = {ArXiv:math/0211262. MR:1977884. Zbl:1033.58009.},
ISSN = {0010-3616},
}
M. Movshev and A. Schwarz :
“On maximally supersymmetric Yang–Mills theories ,”
Nuclear Phys. B
681 : 3
(2004 ),
pp. 324–350 .
MR
2038191
Zbl
1044.81097
ArXiv
hep-th/0311132
article
Abstract
People
BibTeX
We consider ten-dimensional supersymmetric Yang–Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, \( L_{\infty} \) - and \( A_{\infty} \) -algebras.
We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer–Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern–Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra \( (\Omega,\partial) \) of \( (0,k) \) -forms on some supermanifold; the Lie algebra is tensor product of \( (\Omega,\partial) \) and matrix algebra. We construct several other algebras that are quasiisomorphic to \( (\Omega,\partial) \) and, therefore, also can be used to give BV formulation of 10D SUSY YM theory and its reductions. In particular, \( (\Omega,\partial) \) is quasiisomorphic to the algebra \( (B,d) \) , constructed by Berkovits. The algebras \( (\Omega_0,\partial) \) and \( (B_0,d) \) obtained from \( (\Omega,\partial) \) and \( (B,d) \) by means of reduction to a point can be used to give a BV-formulation of IKKT model. We introduce associative algebra SYM as algebra where relations are defined as equations of motion of IKKT model and show that Koszul dual to the algebra \( (B_0,d) \) is quasiisomorphic to SYM.
@article {key2038191m,
AUTHOR = {Movshev, M. and Schwarz, A.},
TITLE = {On maximally supersymmetric {Y}ang--{M}ills
theories},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {681},
NUMBER = {3},
YEAR = {2004},
PAGES = {324--350},
DOI = {10.1016/j.nuclphysb.2003.12.033},
NOTE = {ArXiv:hep-th/0311132. MR:2038191. Zbl:1044.81097.},
ISSN = {0550-3213},
}
A. Schwarz :
“A-model and generalized Chern–Simons theory ,”
Phys. Lett. B
620 : 3–4
(2005 ),
pp. 180–186 .
MR
2149784
Zbl
1247.81441
ArXiv
hep-th/0501119
article
Abstract
BibTeX
@article {key2149784m,
AUTHOR = {Schwarz, A.},
TITLE = {A-model and generalized {C}hern--{S}imons
theory},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters. B. Particle Physics,
Nuclear Physics and Cosmology},
VOLUME = {620},
NUMBER = {3--4},
YEAR = {2005},
PAGES = {180--186},
DOI = {10.1016/j.physletb.2005.06.030},
NOTE = {ArXiv:hep-th/0501119. MR:2149784. Zbl:1247.81441.},
ISSN = {0370-2693},
}
Y. Chen, M. Kontsevich, and A. Schwarz :
“Symmetries of WDVV equations ,”
Nuclear Phys. B
730 : 3
(2005 ),
pp. 352–363 .
MR
2180009
Zbl
1276.81096
ArXiv
hep-th/0508221
article
Abstract
People
BibTeX
We say that a function \( F(\tau) \) obeys WDVV equations, if for a given invertible symmetric matrix \( \eta^{\alpha \beta} \) and all \( \tau \in \mathcal{T} \subset \mathbb{R}^n \) , the expressions
\[ c_{\beta\gamma}^{\alpha}(\tau) = \eta^{\alpha\lambda}\partial_{\lambda}\partial_{\beta}\partial_{\gamma}F \]
can be considered as structure constants of commutative associative algebra; the matrix \( \eta_{\alpha \beta} \) inverse to \( \eta^{\alpha \beta} \) determines an invariant scalar product on this algebra. A function \( x^{\alpha}(z,\tau) \) obeying
\[ \partial_{\alpha}\partial_{\beta} \,x^{\gamma}(z,\tau) = z^{-1}c_{\alpha\beta}^{\epsilon}\partial_{\epsilon}\,x^{\gamma}(z,\tau) \]
is called a calibration of a solution of WDVV equations. We show that there exists an infinite-dimensional group acting on the space of calibrated solutions of WDVV equations (in different form such a group was constructed in [Givental 2004]. We describe the action of Lie algebra of this group.
@article {key2180009m,
AUTHOR = {Chen, Yujun and Kontsevich, Maxim and
Schwarz, Albert},
TITLE = {Symmetries of {WDVV} equations},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {730},
NUMBER = {3},
YEAR = {2005},
PAGES = {352--363},
DOI = {10.1016/j.nuclphysb.2005.09.025},
NOTE = {ArXiv:hep-th/0508221. MR:2180009. Zbl:1276.81096.},
ISSN = {0550-3213},
}
M. Kontsevich, N. Nekrasov, A. Schwarz, M. Shubin, and D. Sternheimer :
“Foreword ,”
pp. 1
in
Special volume dedicated to the memory of F. A. Berezin ,
published as Lett. Math. Phys.
74 : 1 .
Issue edited by N. A. Nekrasov, A. Schwarz, M. Shubin, D. Sternheimer, and M. Kontsevich .
Springer Netherlands (Dordrecht ),
2005 .
MR
2193544
Zbl
1146.00304
incollection
People
BibTeX
@article {key2193544m,
AUTHOR = {Kontsevich, Maxim and Nekrasov, Nikita
and Schwarz, Albert and Shubin, Mikhail
and Sternheimer, Daniel},
TITLE = {Foreword},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {74},
NUMBER = {1},
YEAR = {2005},
PAGES = {1},
DOI = {10.1007/s11005-005-0013-y},
NOTE = {\textit{Special volume dedicated to
the memory of {F}.~{A}. {B}erezin}.
Issue edited by N. A. Nekrasov,
A. Schwarz, M. Shubin, D. Sternheimer,
and M. Kontsevich. MR:2193544.
Zbl:1146.00304.},
ISSN = {0377-9017},
}
S. Gukov, A. Schwarz, and C. Vafa :
“Khovanov–Rozansky homology and topological strings ,”
Lett. Math. Phys.
74 : 1
(2005 ),
pp. 53–74 .
MR
2193547
Zbl
1105.57011
ArXiv
hep-th/0412243
article
Abstract
People
BibTeX
We conjecture a relation between the \( \mathfrak{sl}(N) \) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the \( \mathfrak{sl}(N) \) knot homology groups and suggests that they can be interpreted directly in topological string theory. We use this approach in various examples to predict the \( \mathfrak{sl}(N) \) knot homology groups for all values of \( N \) . We verify that our predictions pass some non-trivial checks.
@article {key2193547m,
AUTHOR = {Gukov, Sergei and Schwarz, Albert and
Vafa, Cumrun},
TITLE = {Khovanov--{R}ozansky homology and topological
strings},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {74},
NUMBER = {1},
YEAR = {2005},
PAGES = {53--74},
DOI = {10.1007/s11005-005-0008-8},
NOTE = {ArXiv:hep-th/0412243. MR:2193547. Zbl:1105.57011.},
ISSN = {0377-9017},
}
A. Schwarz and I. Shapiro :
“Some remarks on Gopakumar–Vafa invariants ,”
pp. 817–826
in
Special issue: In memory of Armand Borel, part 3 ,
published as Pure Appl. Math. Q.
1 : 4 .
International Press (Somerville, MA ),
2005 .
MR
2201001
Zbl
1130.14300
ArXiv
hep-th/0412119
incollection
Abstract
People
BibTeX
@article {key2201001m,
AUTHOR = {Schwarz, A. and Shapiro, I.},
TITLE = {Some remarks on {G}opakumar--{V}afa
invariants},
JOURNAL = {Pure Appl. Math. Q.},
FJOURNAL = {Pure and Applied Mathematics Quarterly},
VOLUME = {1},
NUMBER = {4},
YEAR = {2005},
PAGES = {817--826},
DOI = {10.4310/PAMQ.2005.v1.n4.a5},
NOTE = {\textit{Special issue: {I}n memory of
{A}rmand {B}orel, part 3}. ArXiv:hep-th/0412119.
MR:2201001. Zbl:1130.14300.},
ISSN = {1558-8599},
}
Special volume dedicated to the memory of F. A. Berezin ,
published as Lett. Math. Phys.
74 : 1 .
Issue edited by N. A. Nekrasov, A. Schwarz, M. Shubin, D. Sternheimer, and M. Kontsevich .
Springer Netherlands (Dordrecht ),
October 2005 .
book
People
BibTeX
@book {key68150180,
TITLE = {Special volume dedicated to the memory
of {F}.~{A}. {B}erezin},
EDITOR = {Nekrasov, N. A. and Schwarz, A. and
Shubin, M. and Sternheimer, Daniel and
Kontsevich, Maxim},
PUBLISHER = {Springer Netherlands},
ADDRESS = {Dordrecht},
MONTH = {October},
YEAR = {2005},
PAGES = {109},
URL = {https://link.springer.com/journal/11005/volumes-and-issues/74-1},
NOTE = {Published as \textit{Lett. Math. Phys.}
\textbf{74}:1.},
ISSN = {0377-9017},
}
M. Movshev and A. Schwarz :
“Algebraic structure of Yang–Mills theory ,”
pp. 473–523
in
The unity of mathematics
(Cambridge, MA, 31 August–4 September 2003 ).
Edited by P. Etingof, V. Retakh, and I. M. Singer .
Progress in Mathematics 244 .
Birkhäuser (Boston ),
2006 .
Conference in honor of the ninetieth birthday of I. M. Gelfand.
MR
2181815
Zbl
1229.81281
ArXiv
hep-th/0404183
incollection
Abstract
People
BibTeX
@incollection {key2181815m,
AUTHOR = {Movshev, M. and Schwarz, A.},
TITLE = {Algebraic structure of {Y}ang--{M}ills
theory},
BOOKTITLE = {The unity of mathematics},
EDITOR = {Etingof, Pavel and Retakh, Vladimir
and Singer, I. M.},
SERIES = {Progress in Mathematics},
NUMBER = {244},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston},
YEAR = {2006},
PAGES = {473--523},
DOI = {10.1007/0-8176-4467-9_14},
NOTE = {(Cambridge, MA, 31 August--4 September
2003). Conference in honor of the ninetieth
birthday of I.~M. Gelfand. ArXiv:hep-th/0404183.
MR:2181815. Zbl:1229.81281.},
ISSN = {0743-1643},
ISBN = {9780817644673},
}
M. Kontsevich, A. Schwarz, and V. Vologodsky :
“Integrality of instanton numbers and \( p \) -adic B-model ,”
Phys. Lett. B
637 : 1–2
(2006 ),
pp. 97–101 .
MR
2230876
Zbl
1247.14058
ArXiv
hep-th/0603106
article
Abstract
People
BibTeX
Vadim Aleksandrovich Vologodsky
Related
Maksim Lvovich Kontsevich
Related
@article {key2230876m,
AUTHOR = {Kontsevich, Maxim and Schwarz, Albert
and Vologodsky, Vadim},
TITLE = {Integrality of instanton numbers and
\$p\$-adic {B}-model},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters. B. Particle Physics,
Nuclear Physics and Cosmology},
VOLUME = {637},
NUMBER = {1--2},
YEAR = {2006},
PAGES = {97--101},
DOI = {10.1016/j.physletb.2006.04.012},
NOTE = {ArXiv:hep-th/0603106. MR:2230876. Zbl:1247.14058.},
ISSN = {0370-2693},
}
A. Schwarz and I. Shapiro :
“Supergeometry and arithmetic geometry ,”
Nuclear Phys. B
756 : 3
(2006 ),
pp. 207–218 .
MR
2268062
Zbl
1215.14016
ArXiv
hep-th/0605119
article
Abstract
People
BibTeX
@article {key2268062m,
AUTHOR = {Schwarz, A. and Shapiro, I.},
TITLE = {Supergeometry and arithmetic geometry},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {756},
NUMBER = {3},
YEAR = {2006},
PAGES = {207--218},
DOI = {10.1016/j.nuclphysb.2006.08.024},
NOTE = {ArXiv:hep-th/0605119. MR:2268062. Zbl:1215.14016.},
ISSN = {0550-3213},
}
A. Schwarz and X. Tang :
“Quantization and holomorphic anomaly ,”
J. High Energy Phys.
2007 : 3
(2007 ),
pp. article no. 062, 18 pages .
MR
2313939
ArXiv
hep-th/0611281
article
Abstract
People
BibTeX
@article {key2313939m,
AUTHOR = {Schwarz, Albert and Tang, Xiang},
TITLE = {Quantization and holomorphic anomaly},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {2007},
NUMBER = {3},
YEAR = {2007},
PAGES = {article no. 062, 18 pages},
DOI = {10.1088/1126-6708/2007/03/062},
NOTE = {ArXiv:hep-th/0611281. MR:2313939.},
ISSN = {1126-6708},
}
A. Schwarz and V. Vologodsky :
“Frobenius transformation, mirror map and instanton numbers ,”
Phys. Lett. B
660 : 4
(2008 ),
pp. 422–427 .
MR
2396265
Zbl
1246.14053
ArXiv
hep-th/0606151
article
Abstract
People
BibTeX
Vadim Aleksandrovich Vologodsky
Related
@article {key2396265m,
AUTHOR = {Schwarz, Albert and Vologodsky, Vadim},
TITLE = {Frobenius transformation, mirror map
and instanton numbers},
JOURNAL = {Phys. Lett. B},
FJOURNAL = {Physics Letters. B. Particle Physics,
Nuclear Physics and Cosmology},
VOLUME = {660},
NUMBER = {4},
YEAR = {2008},
PAGES = {422--427},
DOI = {10.1016/j.physletb.2008.01.006},
NOTE = {ArXiv:hep-th/0606151. MR:2396265. Zbl:1246.14053.},
ISSN = {0370-2693},
}
A. Schwarz and I. Shapiro :
“\( p \) -adic superspaces and Frobenius ,”
Comm. Math. Phys.
282 : 1
(2008 ),
pp. 87–113 .
MR
2415474
Zbl
1202.14017
ArXiv
math/0605310
article
Abstract
People
BibTeX
The notion of a \( p \) -adic superspace is introduced and used to give a transparent construction of the Frobenius map on \( p \) -adic cohomology of a smooth projective variety over \( \mathbb{Z}_p \) (the ring of \( p \) -adic integers), as well as an alternative construction of the crystalline cohomology of a smooth projective variety over \( \mathbb{F}_p \) (finite field with \( p \) elements).
@article {key2415474m,
AUTHOR = {Schwarz, A. and Shapiro, I.},
TITLE = {\$p\$-adic superspaces and {F}robenius},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {282},
NUMBER = {1},
YEAR = {2008},
PAGES = {87--113},
DOI = {10.1007/s00220-008-0526-1},
NOTE = {ArXiv:math/0605310. MR:2415474. Zbl:1202.14017.},
ISSN = {0010-3616},
}
A. Schwarz and I. Shapiro :
“Twisted de Rham cohomology, homological definition of the integral and ‘physics over a ring’ ,”
Nuclear Phys. B
809 : 3
(2009 ),
pp. 547–560 .
MR
2478121
Zbl
1192.81311
ArXiv
0809.0086
article
Abstract
People
BibTeX
We use the notion of the twisted de Rham cohomology to give meaning to an integral of the form
\[ \int g(x) e^{f(x)} dx \]
over an arbitrary ring. We discuss also a definition of a family of integrals and some properties of the above homological definition of the integral. We show how to use the twisted de Rham cohomology to define the Frobenius map on the \( p \) -adic cohomology. Finally, we consider two-dimensional topological quantum field theories with general coefficients.
@article {key2478121m,
AUTHOR = {Schwarz, A. and Shapiro, I.},
TITLE = {Twisted de {R}ham cohomology, homological
definition of the integral and ``physics
over a ring''},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {809},
NUMBER = {3},
YEAR = {2009},
PAGES = {547--560},
DOI = {10.1016/j.nuclphysb.2008.10.005},
NOTE = {ArXiv:0809.0086. MR:2478121. Zbl:1192.81311.},
ISSN = {0550-3213},
}
A. Schwarz and V. Vologodsky :
“Integrality theorems in the theory of topological strings ,”
Nuclear Phys. B
821 : 3
(2009 ),
pp. 506–534 .
MR
2547214
Zbl
1203.81155
ArXiv
0807.1714
article
Abstract
People
BibTeX
Vadim Aleksandrovich Vologodsky
Related
@article {key2547214m,
AUTHOR = {Schwarz, Albert and Vologodsky, Vadim},
TITLE = {Integrality theorems in the theory of
topological strings},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {821},
NUMBER = {3},
YEAR = {2009},
PAGES = {506--534},
DOI = {10.1016/j.nuclphysb.2009.05.014},
NOTE = {ArXiv:0807.1714. MR:2547214. Zbl:1203.81155.},
ISSN = {0550-3213},
}
A. Schwarz :
“Space and time from translation symmetry ,”
J. Math. Phys.
51 : 1
(2010 ),
pp. article no. 015201, 7 pages .
MR
2605834
Zbl
1245.81070
ArXiv
hep-th/0601035
article
Abstract
BibTeX
@article {key2605834m,
AUTHOR = {Schwarz, A.},
TITLE = {Space and time from translation symmetry},
JOURNAL = {J. Math. Phys.},
FJOURNAL = {Journal of Mathematical Physics},
VOLUME = {51},
NUMBER = {1},
YEAR = {2010},
PAGES = {article no. 015201, 7 pages},
DOI = {10.1063/1.3257623},
NOTE = {ArXiv:hep-th/0601035. MR:2605834. Zbl:1245.81070.},
ISSN = {0022-2488},
}
M. Movshev, A. Schwarz, and R. Xu :
Homology of Lie algebra of supersymmetries .
Preprint ,
2010 .
ArXiv
1011.4731
techreport
People
BibTeX
@techreport {key1011.4731a,
AUTHOR = {Movshev, Michael and Schwarz, Albert
and Xu, Renjun},
TITLE = {Homology of Lie algebra of supersymmetries},
TYPE = {preprint},
YEAR = {2010},
NOTE = {ArXiv:1011.4731.},
}
M. V. Movshev and A. Schwarz :
“Maximal supersymmetry ,”
pp. 175–193
in
Supersymmetry in mathematics and physics
(Los Angeles, 6–7 February 2010 ).
Edited by S. Ferrara, R. Fioresi, and V. S. Varadarajan .
Lecture Notes in Mathematics 2027 .
Springer (Berlin ),
2011 .
MR
2906343
Zbl
1246.81380
incollection
Abstract
People
BibTeX
We have studied supersymmetric and super Poincaré invariant deformations of maximally supersymmetric gauge theories, in particular, of ten-dimensional super Yang–Mills theory and of its reduction to a point. We have described all infinitesimal super Poincaré invariant deformations of equations of motion and proved that all of them are Lagrangian deformations and all of them can be extended to formal deformations. Our methods are based on homological algebra, in particular, on the theory of \( L_{\infty} \) and \( A_{\infty} \) -infinity algebras. In this paper we formulate some of the results we have obtained, but skip all proofs. However, we describe the results of the theory of \( L_{\infty} \) and \( A_{\infty} \) algebras that serve as the main tool in our calculations.
@incollection {key2906343m,
AUTHOR = {Movshev, M. V. and Schwarz, A.},
TITLE = {Maximal supersymmetry},
BOOKTITLE = {Supersymmetry in mathematics and physics},
EDITOR = {Ferrara, Sergio and Fioresi, Rita and
Varadarajan, V. S.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {2027},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2011},
PAGES = {175--193},
DOI = {10.1007/978-3-642-21744-9_9},
NOTE = {(Los Angeles, 6--7 February 2010). MR:2906343.
Zbl:1246.81380.},
ISSN = {0075-8434},
ISBN = {9783642217432},
}
M. V. Movshev, A. Schwarz, and R. Xu :
“Homology of Lie algebra of supersymmetries and of super Poincaré Lie algebra ,”
Nuclear Phys. B
854 : 2
(2012 ),
pp. 483–503 .
MR
2844329
Zbl
1229.81117
ArXiv
1106.0335
article
Abstract
People
BibTeX
We study the homology and cohomology groups of super Lie algebras of supersymmetries and of super Poincaré Lie algebras in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions \( \leq 11 \) . For dimensions \( D = 10,\,11 \) we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry Lie algebras.
@article {key2844329m,
AUTHOR = {Movshev, M. V. and Schwarz, A. and Xu,
Renjun},
TITLE = {Homology of {L}ie algebra of supersymmetries
and of super {P}oincar\'e {L}ie algebra},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {854},
NUMBER = {2},
YEAR = {2012},
PAGES = {483--503},
DOI = {10.1016/j.nuclphysb.2011.08.023},
NOTE = {ArXiv:1106.0335. MR:2844329. Zbl:1229.81117.},
ISSN = {0550-3213},
}
J.-M. Liou and A. Schwarz :
“Equivariant cohomology of infinite-dimensional Grassmannian and shifted Schur functions ,”
Math. Res. Lett.
19 : 4
(2012 ),
pp. 775–784 .
MR
3008414
Zbl
1300.14025
ArXiv
1201.2554
article
Abstract
People
BibTeX
@article {key3008414m,
AUTHOR = {Liou, Jia-Ming and Schwarz, Albert},
TITLE = {Equivariant cohomology of infinite-dimensional
{G}rassmannian and shifted {S}chur functions},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {19},
NUMBER = {4},
YEAR = {2012},
PAGES = {775--784},
DOI = {10.4310/MRL.2012.v19.n4.a4},
NOTE = {ArXiv:1201.2554. MR:3008414. Zbl:1300.14025.},
ISSN = {1073-2780},
}
M. V. Movshev and A. Schwarz :
“Supersymmetric deformations of maximally supersymmetric gauge theories ,”
J. High Energy Phys.
2012 : 9
(2012 ),
pp. article no. 136, 77 pages .
MR
3044913
Zbl
1397.81390
ArXiv
0910.0620
article
Abstract
People
BibTeX
We study supersymmetric and super Poincaré invariant deformations of tendimensional super Yang–Mills theory and of its dimensional reductions. We describe all infinitesimal super Poincaré invariant deformations of equations of motion of ten-dimensional super Yang–Mills theory and deformations of the reduction to a point. We also discuss how these infinitesimals can be extended to formal deformations. Our methods are based on homological algebra, in particular, on the theory of \( L_{\infty} \) and \( A_{\infty} \) algebras. The exposition of this theory as well as of some basic facts about Lie algebra homology and Hochschild homology is given in appendices.
@article {key3044913m,
AUTHOR = {Movshev, M. V. and Schwarz, A.},
TITLE = {Supersymmetric deformations of maximally
supersymmetric gauge theories},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {2012},
NUMBER = {9},
YEAR = {2012},
PAGES = {article no. 136, 77 pages},
DOI = {10.1007/JHEP09(2012)136},
NOTE = {ArXiv:0910.0620. MR:3044913. Zbl:1397.81390.},
ISSN = {1126-6708},
}
J.-M. Liou and A. Schwarz :
“Moduli spaces and Grassmannian ,”
Lett. Math. Phys.
103 : 6
(2013 ),
pp. 585–603 .
MR
3054647
Zbl
1276.14016
ArXiv
1111.1649
article
Abstract
People
BibTeX
@article {key3054647m,
AUTHOR = {Liou, Jia-Ming and Schwarz, A.},
TITLE = {Moduli spaces and {G}rassmannian},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {103},
NUMBER = {6},
YEAR = {2013},
PAGES = {585--603},
DOI = {10.1007/s11005-013-0623-8},
NOTE = {ArXiv:1111.1649. MR:3054647. Zbl:1276.14016.},
ISSN = {0377-9017},
}
A. Mikhailov, A. Schwarz, and R. Xu :
“Cohomology ring of the BRST operator associated to the sum of two pure spinors ,”
Modern Phys. Lett. A
28 : 23
(2013 ),
pp. article no. 1350107, 6 pages .
MR
3085958
Zbl
1279.81052
ArXiv
1305.0071
article
Abstract
People
BibTeX
In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.
@article {key3085958m,
AUTHOR = {Mikhailov, Andrei and Schwarz, Albert
and Xu, Renjun},
TITLE = {Cohomology ring of the {BRST} operator
associated to the sum of two pure spinors},
JOURNAL = {Modern Phys. Lett. A},
FJOURNAL = {Modern Physics Letters A. Particles
and Fields, Gravitation, Cosmology,
Nuclear Physics},
VOLUME = {28},
NUMBER = {23},
YEAR = {2013},
PAGES = {article no. 1350107, 6 pages},
DOI = {10.1142/S0217732313501071},
NOTE = {ArXiv:1305.0071. MR:3085958. Zbl:1279.81052.},
ISSN = {0217-7323},
}
D. Krefl and A. Schwarz :
“Refined Chern–Simons versus Vogel universality ,”
J. Geom. Phys.
74
(2013 ),
pp. 119–129 .
MR
3118578
Zbl
1283.58018
ArXiv
1304.7873
article
Abstract
People
BibTeX
@article {key3118578m,
AUTHOR = {Krefl, Daniel and Schwarz, Albert},
TITLE = {Refined {C}hern--{S}imons versus {V}ogel
universality},
JOURNAL = {J. Geom. Phys.},
FJOURNAL = {Journal of Geometry and Physics},
VOLUME = {74},
YEAR = {2013},
PAGES = {119--129},
DOI = {10.1016/j.geomphys.2013.08.002},
NOTE = {ArXiv:1304.7873. MR:3118578. Zbl:1283.58018.},
ISSN = {0393-0440},
}
R. Xu, M. Movshev, and A. Schwarz :
“Integral invariants in flat superspace ,”
Nuclear Phys. B
884
(2014 ),
pp. 28–43 .
MR
3214872
Zbl
1323.81093
ArXiv
1403.1997
article
Abstract
People
BibTeX
We are solving for the case of flat superspace some homological problems that were formulated by Berkovits and Howe. (Our considerations can be applied also to the case of supertorus.) These problems arise in the attempt to construct integrals invariant with respect to supersymmetry. They appear also in other situations, in particular, in the pure spinor formalism in supergravity.
@article {key3214872m,
AUTHOR = {Xu, Renjun and Movshev, Michael and
Schwarz, Albert},
TITLE = {Integral invariants in flat superspace},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B.},
VOLUME = {884},
YEAR = {2014},
PAGES = {28--43},
DOI = {10.1016/j.nuclphysb.2014.04.009},
NOTE = {ArXiv:1403.1997. MR:3214872. Zbl:1323.81093.},
ISSN = {0550-3213},
}
X. Liu and A. Schwarz :
Quantization of classical curves .
Preprint ,
March 2014 .
ArXiv
1403.1000
techreport
Abstract
People
BibTeX
We discuss the relation between quantum curves (defined as solutions of equation \( [P,Q] = \hbar \) , where \( P \) , \( Q \) are ordinary differential operators) and classical curves. We illustrate this relation for the case of quantum curve that corresponds to the \( (p,q) \) -minimal model coupled to 2D gravity.
@techreport {key1403.1000a,
AUTHOR = {Liu, Xiaojun and Schwarz, Albert},
TITLE = {Quantization of classical curves},
TYPE = {Preprint},
MONTH = {March},
YEAR = {2014},
PAGES = {10},
URL = {https://arxiv.org/pdf/1403.1000},
NOTE = {ArXiv:1403.1000.},
}
A. Schwarz :
“Quantum curves ,”
Comm. Math. Phys.
338 : 1
(2015 ),
pp. 483–500 .
MR
3345383
Zbl
1318.81042
ArXiv
1401.1574
article
Abstract
BibTeX
One says that a pair \( (P,Q) \) of ordinary differential operators specify a quantum curve if \( [P,Q] = \hbar \) . If a pair of difference operators \( (K,L) \) obey the relation
\[ KL = qLK \quad \text{where }q = e^{\hbar} ,\]
we say that they specify a discrete quantum curve.
This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions.
The goal of this paper is to study the moduli spaces of quantum curves. We will relate the moduli spaces for different \( \hbar \) . We will show how to quantize a pair of commuting differential or difference operators (i.e., to construct the corresponding quantum curve or discrete quantum curve).
@article {key3345383m,
AUTHOR = {Schwarz, Albert},
TITLE = {Quantum curves},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {338},
NUMBER = {1},
YEAR = {2015},
PAGES = {483--500},
DOI = {10.1007/s00220-015-2287-y},
NOTE = {ArXiv:1401.1574. MR:3345383. Zbl:1318.81042.},
ISSN = {0010-3616},
}
J.-M. Liou, A. Schwarz, and R. Xu :
“Weierstrass cycles and tautological rings in various moduli spaces of algebraic curves ,”
J. Fixed Point Theory Appl.
17 : 1
(2015 ),
pp. 209–219 .
To Professor Andrzej Granas.
MR
3392990
Zbl
1345.14042
ArXiv
1308.6374
article
Abstract
People
BibTeX
We analyze Weierstrass cycles and tautological rings in moduli spaces of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus less than or equal to 6. In particular, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for low genera.
@article {key3392990m,
AUTHOR = {Liou, Jia-Ming and Schwarz, Albert and
Xu, Renjun},
TITLE = {Weierstrass cycles and tautological
rings in various moduli spaces of algebraic
curves},
JOURNAL = {J. Fixed Point Theory Appl.},
FJOURNAL = {Journal of Fixed Point Theory and Applications},
VOLUME = {17},
NUMBER = {1},
YEAR = {2015},
PAGES = {209--219},
DOI = {10.1007/s11784-015-0241-4},
NOTE = {To Professor Andrzej Granas. ArXiv:1308.6374.
MR:3392990. Zbl:1345.14042.},
ISSN = {1661-7738},
}
A. Schwarz, V. Vologodsky, and J. Walcher :
“Framing the di-logarithm (over \( \mathbb{Z} \) ) ,”
pp. 113–128
in
String-Math 2012
(Bonn, Germany, 16–21 July 2012 ).
Edited by R. Donagi, S. Katz, A. Klemm, and D. R. Morrison .
Proceedings of Symposia in Pure Mathematics 90 .
American Mathematical Society (Providence, RI ),
2015 .
MR
3409790
Zbl
1356.81196
ArXiv
1306.4298
incollection
Abstract
People
BibTeX
Motivated by their role for integrality and integrability in topological string theory, we introduce the general mathematical notion of “\( s \) -functions” as integral linear combinations of poly-logarithms. 2-functions arise as disk amplitudes in Calabi–Yau D-brane backgrounds and form the simplest and most important special class. We describe \( s \) -functions in terms of the action of the Frobenius endomorphism on formal power series and use this description to characterize 2-functions in terms of algebraic K-theory of the completed power series ring. This characterization leads to a general proof of integrality of the framing transformation, via a certain orthogonality relation in K-theory. We comment on a variety of possible applications. We here consider only power series with rational coefficients; the general situation when the coefficients belong to an arbitrary algebraic number field is treated in a companion paper.
@incollection {key3409790m,
AUTHOR = {Schwarz, Albert and Vologodsky, Vadim
and Walcher, Johannes},
TITLE = {Framing the di-logarithm (over \$\mathbb{Z}\$)},
BOOKTITLE = {String-{M}ath 2012},
EDITOR = {Donagi, Ron and Katz, Sheldon and Klemm,
Albrecht and Morrison, David R.},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {90},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2015},
PAGES = {113--128},
DOI = {10.1090/pspum/090/01532},
NOTE = {(Bonn, Germany, 16--21 July 2012). ArXiv:1306.4298.
MR:3409790. Zbl:1356.81196.},
ISSN = {0082-0717},
ISBN = {9780821894958},
}
M. V. Movshev and A. Schwarz :
“Generalized Chern–Simons action and maximally supersymmetric gauge theories ,”
pp. 327–340
in
String-Math 2012
(Bonn, Germany, 16–21 July 2012 ).
Edited by R. Donagi, S. Katz, A. Klemm, and D. R. Morrison .
Proceedings of Symposia in Pure Mathematics 90 .
American Mathematical Society (Providence, RI ),
2015 .
MR
3409803
Zbl
1356.81200
ArXiv
1304.7500
incollection
Abstract
People
BibTeX
@incollection {key3409803m,
AUTHOR = {Movshev, M. V. and Schwarz, A.},
TITLE = {Generalized {C}hern--{S}imons action
and maximally supersymmetric gauge theories},
BOOKTITLE = {String-{M}ath 2012},
EDITOR = {Donagi, Ron and Katz, Sheldon and Klemm,
Albrecht and Morrison, David R.},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {90},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2015},
PAGES = {327--340},
DOI = {10.1090/pspum/090/01527},
NOTE = {(Bonn, Germany, 16--21 July 2012). ArXiv:1304.7500.
MR:3409803. Zbl:1356.81200.},
ISSN = {0082-0717},
ISBN = {9780821894958},
}
A. Schwarz :
“Axiomatic conformal theory in dimensions \( > 2 \) and AdS/CT correspondence ,”
Lett. Math. Phys.
106 : 9
(2016 ),
pp. 1181–1197 .
MR
3533564
Zbl
1347.81058
ArXiv
1509.08064
article
Abstract
BibTeX
We formulate axioms of conformal theory (CT) in dimensions \( > 2 \) modifying Segal’s axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT, one includes also a condition of existence of energy-momentum tensor.) We use these axioms to derive the AdS/CT correspondence for local theories on AdS. We introduce a notion of weakly local quantum field theory and construct a bijective correspondence between conformal theories on the sphere \( S^d \) and weakly local quantum field theories on \( H^{d+1} \) that are invariant with respect to isometries. (Here \( H^{d+1} \) denotes hyperbolic space = Euclidean AdS space.) We give an expression of AdS correlation functions in terms of CT correlation functions. The conformal theory has conserved energy-momentum tensor iff the AdS theory has graviton in its spectrum.
@article {key3533564m,
AUTHOR = {Schwarz, Albert},
TITLE = {Axiomatic conformal theory in dimensions
\$>2\$ and {A}d{S}/{CT} correspondence},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics},
VOLUME = {106},
NUMBER = {9},
YEAR = {2016},
PAGES = {1181--1197},
DOI = {10.1007/s11005-016-0866-2},
NOTE = {ArXiv:1509.08064. MR:3533564. Zbl:1347.81058.},
ISSN = {0377-9017},
}
M. T. Luu and A. Schwarz :
“Fourier duality of quantum curves ,”
Math. Res. Lett.
23 : 4
(2016 ),
pp. 1111–1137 .
MR
3554503
Zbl
1354.81040
ArXiv
1504.01582
article
Abstract
People
BibTeX
@article {key3554503m,
AUTHOR = {Luu, Martin T. and Schwarz, Albert},
TITLE = {Fourier duality of quantum curves},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {23},
NUMBER = {4},
YEAR = {2016},
PAGES = {1111--1137},
DOI = {10.4310/MRL.2016.v23.n4.a7},
NOTE = {ArXiv:1504.01582. MR:3554503. Zbl:1354.81040.},
ISSN = {1073-2780},
}
A. Mikhailov and A. Schwarz :
“Families of gauge conditions in BV formalism ,”
J. High Energy Phys.
2017 : 7
(2017 ),
pp. article no. 063, 25 pages .
MR
3686735
Zbl
1380.81371
ArXiv
1610.02996
article
Abstract
People
BibTeX
@article {key3686735m,
AUTHOR = {Mikhailov, Andrei and Schwarz, Albert},
TITLE = {Families of gauge conditions in {BV}
formalism},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {2017},
NUMBER = {7},
YEAR = {2017},
PAGES = {article no. 063, 25 pages},
DOI = {10.1007/JHEP07(2017)063},
NOTE = {ArXiv:1610.02996. MR:3686735. Zbl:1380.81371.},
ISSN = {1126-6708},
}
J.-M. Liou and A. Schwarz :
“Weierstrass cycles in moduli spaces and the Krichever map ,”
Math. Res. Lett.
24 : 6
(2017 ),
pp. 1739–1758 .
MR
3762693
Zbl
1393.14022
ArXiv
1207.0530
article
Abstract
People
BibTeX
@article {key3762693m,
AUTHOR = {Liou, Jia-Ming and Schwarz, Albert},
TITLE = {Weierstrass cycles in moduli spaces
and the {K}richever map},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {24},
NUMBER = {6},
YEAR = {2017},
PAGES = {1739--1758},
DOI = {10.4310/MRL.2017.v24.n6.a9},
NOTE = {ArXiv:1207.0530. MR:3762693. Zbl:1393.14022.},
ISSN = {1073-2780},
}
A. Schwarz, V. Vologodsky, and J. Walcher :
Integrality of framing and geometric origin of 2-functions .
Preprint ,
February 2017 .
ArXiv
1702.07135
techreport
Abstract
People
BibTeX
We say that a formal power series \( \sum a_n z^n \) with rational coefficients is a 2-function if the numerator of the fraction \( a_{n/p} - p^2 a_n \) is divisible by \( p^2 \) for every prime number \( p \) . One can prove that 2-functions with rational coefficients appear as building block of BPS generating functions in topological string theory. Using the Frobenius map we define 2-functions with coefficients in algebraic number fields. We establish two results pertaining to these functions. First, we show that the class of 2-functions is closed under the so-called framing operation (related to compositional inverse of power series). Second, we show that 2-functions arise naturally in geometry as \( q \) -expansion of the truncated normal function associated with an algebraic cycle extending a degenerating family of Calabi–Yau 3-folds.
@techreport {key1702.07135a,
AUTHOR = {Schwarz, Albert and Vologodsky, Vadim
and Walcher, Johannes},
TITLE = {Integrality of framing and geometric
origin of 2-functions},
TYPE = {Preprint},
MONTH = {February},
YEAR = {2017},
PAGES = {66},
URL = {https://arxiv.org/pdf/1702.07135.pdf},
NOTE = {ArXiv:1702.07135.},
}
M. Movshev and A. Schwarz :
“Quantum deformation of planar amplitudes ,”
J. High Energy Phys.
2018 : 4
(2018 ).
article no. 121, 20 pages.
MR
3801153
Zbl
1390.81613
ArXiv
1711.10053
article
Abstract
People
BibTeX
In maximally supersymmetric four-dimensional gauge theories planar on-shell diagrams are closely related to the positive Grassmannian and the cell decomposition of it into the union of so called positroid cells. (This was proven by N. Arkani-Hamed, J. Bourjaily, F. Cachazo, A. Goncharov, A. Postnikov, and J. Trnka.) We establish that volume forms on positroids used to express scattering amplitudes can be \( q \) -deformed to Hochschild homology classes of corresponding quantum algebras. The planar amplitudes are represented as sums of contributions of some set of positroid cells; we quantize these contributions. In classical limit our considerations allow us to obtain explicit formulas for contributions of positroid cells to scattering amplitudes.
@article {key3801153m,
AUTHOR = {Movshev, M. and Schwarz, A.},
TITLE = {Quantum deformation of planar amplitudes},
JOURNAL = {J. High Energy Phys.},
FJOURNAL = {Journal of High Energy Physics},
VOLUME = {2018},
NUMBER = {4},
YEAR = {2018},
DOI = {10.1007/jhep04(2018)121},
NOTE = {article no. 121, 20 pages. ArXiv:1711.10053.
MR:3801153. Zbl:1390.81613.},
ISSN = {1126-6708},
}
A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, and A. N. Shiryaev :
“Vladimir Antonovich Zorich (on his 80th birthday) ,”
Usp. Mat. Nauk
73 : 5(443)
(2018 ),
pp. 193–196 .
An English translation was published in Russ. Math. Surv. 73 :5 (2018) .
MR
3859406
article
People
BibTeX
@article {key3859406m,
AUTHOR = {Aptekarev, A. I. and Buchstaber, V.
M. and Vassiliev, V. A. and Gromov,
M. L. and Ilyashenko, Yu. S. and Kashin,
B. S. and Keselman, V. M. and Kozlov,
V. V. and Kontsevich, M. L. and Krichever,
I. M. and Kruzhilin, N. G. and Lando,
S. K. and Manin, Yu. I. and Margulis,
G. A. and Nemirovski, S. Yu. and Novikov,
S. P. and Reshetnyak, Yu. G. and Sinai,
Ya. G. and Suetin, S. P. and Treschev,
D. V. and Fuchs, D. B. and Khovanskii,
A. G. and Chirka, E. M. and Schwarz,
A. S. and Shiryaev, A. N.},
TITLE = {Vladimir {A}ntonovich {Z}orich (on his
80th birthday)},
JOURNAL = {Usp. Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk},
VOLUME = {73},
NUMBER = {5(443)},
YEAR = {2018},
PAGES = {193--196},
DOI = {10.4213/rm9828},
NOTE = {An English translation was published
in \textit{Russ. Math. Surv.} \textbf{73}:5
(2018). MR:3859406.},
ISSN = {0042-1316},
}
A. Schwarz :
“Les supermathématiques et la physique ”
[Supermathematics and physics ],
pp. 137–141
in
Les “supermathématiques” et F. A. Berezin
[“Supermathematics” and F. A. Berezin ].
Edited by C. Anné and V. Roubtsov .
La Série T .
Société Mathématique de France (Paris ),
2018 .
MR
3930445
incollection
People
BibTeX
@incollection {key3930445m,
AUTHOR = {Schwarz, Albert},
TITLE = {Les supermath\'ematiques et la physique
[Supermathematics and physics]},
BOOKTITLE = {Les ``supermath\'ematiques'' et {F}.~{A}.
{B}erezin [``Supermathematics'' and
{F}.~{A}. {B}erezin]},
EDITOR = {Ann\'e, Colette and Roubtsov, Volodya},
SERIES = {La S\'erie T},
PUBLISHER = {Soci\'et\'e Math\'ematique de France},
ADDRESS = {Paris},
YEAR = {2018},
PAGES = {137--141},
NOTE = {MR:3930445.},
ISSN = {2109-7186},
ISBN = {9782856298336},
}
A. I. Aptekarev, V. M. Buchstaber, V. A. Vassiliev, M. L. Gromov, Yu. S. Ilyashenko, B. S. Kashin, V. M. Keselman, V. V. Kozlov, M. L. Kontsevich, I. M. Krichever, N. G. Kruzhilin, S. K. Lando, Yu. I. Manin, G. A. Margulis, S. Yu. Nemirovski, S. P. Novikov, Yu. G. Reshetnyak, Ya. G. Sinai, S. P. Suetin, D. V. Treschev, D. B. Fuchs, A. G. Khovanskii, E. M. Chirka, A. S. Schwarz, and A. N. Shiryaev :
“Vladimir Antonovich Zorich (on his 80th birthday) ,”
Russ. Math. Surv.
73 : 5
(2018 ),
pp. 935–939 .
English translation of Russian original published in Usp. Mat. Nauk 73 :5(443) (2018) .
Zbl
1417.01018
article
People
BibTeX
@article {key1417.01018z,
AUTHOR = {Aptekarev, A. I. and Buchstaber, V.
M. and Vassiliev, V. A. and Gromov,
M. L. and Ilyashenko, Yu. S. and Kashin,
B. S. and Keselman, V. M. and Kozlov,
V. V. and Kontsevich, M. L. and Krichever,
I. M. and Kruzhilin, N. G. and Lando,
S. K. and Manin, Yu. I. and Margulis,
G. A. and Nemirovski, S. Yu. and Novikov,
S. P. and Reshetnyak, Yu. G. and Sinai,
Ya. G. and Suetin, S. P. and Treschev,
D. V. and Fuchs, D. B. and Khovanskii,
A. G. and Chirka, E. M. and Schwarz,
A. S. and Shiryaev, A. N.},
TITLE = {Vladimir {A}ntonovich {Z}orich (on his
80th birthday)},
JOURNAL = {Russ. Math. Surv.},
FJOURNAL = {Russian Mathematical Surveys},
VOLUME = {73},
NUMBER = {5},
YEAR = {2018},
PAGES = {935--939},
DOI = {10.1070/RM9828},
NOTE = {English translation of Russian original
published in \textit{Usp. Mat. Nauk}
\textbf{73}:5(443) (2018). Zbl:1417.01018.},
ISSN = {0036-0279},
}
M. Luu and A. Schwarz :
Iterated integrals on affine curves .
Preprint ,
December 2019 .
ArXiv
1912.09506
techreport
Abstract
People
BibTeX
@techreport {key1912.09506a,
AUTHOR = {Luu, Martin and Schwarz, Albert},
TITLE = {Iterated integrals on affine curves},
TYPE = {Preprint},
MONTH = {December},
YEAR = {2019},
PAGES = {10},
URL = {https://arxiv.org/pdf/1912.09506.pdf},
NOTE = {ArXiv:1912.09506.},
}
A. Schwarz :
Scattering matrix and inclusive scattering matrix in algebraic quantum field theory .
Preprint ,
August 2019 .
To Maxim Kontsevich on the occasion of his 55th birthday with love and admiration.
ArXiv
1908.09388
techreport
Abstract
People
BibTeX
We study the scattering of particles and quasiparticles in the framework of algebraic quantum field theory. The main novelty is the construction of inclusive scattering matrix related to inclusive cross-sections. The inclusive scattering matrix can be expressed in terms of generalized Green functions by a formula similar to the LSZ formula for the conventional scattering matrix.
The consideration of inclusive scattering matrix is necessary in quantum field theory if a unitary scattering matrix does not exist (if the theory does not have particle interpretation). It is always necessary if we want to consider collisions of quasiparticles.
@techreport {key1908.09388a,
AUTHOR = {Schwarz, Albert},
TITLE = {Scattering matrix and inclusive scattering
matrix in algebraic quantum field theory},
TYPE = {Preprint},
MONTH = {August},
YEAR = {2019},
PAGES = {14},
URL = {https://arxiv.org/pdf/1908.09388.pdf},
NOTE = {To Maxim Kontsevich on the occasion
of his 55th birthday with love and admiration.
ArXiv:1908.09388.},
}
A. Schwarz :
“Inclusive scattering matrix and scattering of quasiparticles ,”
Nuclear Phys. B
950
(2020 ).
article no. 114869, 14 pages.
MR
4039472
ArXiv
1904.04050
article
Abstract
BibTeX
The quantum theory can be formulated in the language of positive functionals on Weyl or Clifford algebra (\( L \) -functionals). It is shown that this language gives simple understanding of diagrams of Keldysh formalism (that coincide in our case with the diagrams of thermo-field dynamics). The matrix elements of the scattering matrix in the formalism of \( L \) -functionals are related to inclusive cross-sections, therefore we suggest the name “inclusive scattering matrix” for this notion. The inclusive scattering matrix can be expressed in terms of on-shell values of generalized Green functions. This notion is necessary if we want to analyze collisions of quasiparticles.
@article {key4039472m,
AUTHOR = {Schwarz, A.},
TITLE = {Inclusive scattering matrix and scattering
of quasiparticles},
JOURNAL = {Nuclear Phys. B},
FJOURNAL = {Nuclear Physics B},
VOLUME = {950},
YEAR = {2020},
DOI = {10.1016/j.nuclphysb.2019.114869},
NOTE = {article no. 114869, 14 pages. ArXiv:1904.04050.
MR:4039472.},
ISSN = {0550-3213},
}
A. Schwarz :
“Geometric approach to quantum theory ”
in
Special issue on algebra, topology, and dynamics in interaction in honor of Dmitry Fuchs ,
published as SIGMA, Symmetry Integrability Geom. Methods Appl.
16 .
Issue edited by B. Khesin, F. Malikov, V. Ovsienko, and S. Tabachnikov .
National Academy of Sciences of Ukraine (Kiev ),
2020 .
Paper no. 020, 3 pages.
MR
4080799
Zbl
1436.81018
ArXiv
1906.04939
incollection
Abstract
People
BibTeX
@article {key4080799m,
AUTHOR = {Schwarz, Albert},
TITLE = {Geometric approach to quantum theory},
JOURNAL = {SIGMA, Symmetry Integrability Geom.
Methods Appl.},
FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry.
Methods and Applications},
VOLUME = {16},
YEAR = {2020},
DOI = {10.3842/SIGMA.2020.020},
NOTE = {\textit{Special issue on algebra, topology,
and dynamics in interaction in honor
of {D}mitry {F}uchs}. Issue edited by
B. Khesin, F. Malikov,
V. Ovsienko, and S. Tabachnikov.
Paper no. 020, 3 pages. ArXiv:1906.04939.
MR:4080799. Zbl:1436.81018.},
ISSN = {1815-0659},
}
A. M. Astashov, I. V. Astashova, A. V. Bocharov, V. M. Buchstaber, V. A. Vassiliev, A. M. Verbovetsky, A. M. Vershik, A. P. Veselov, M. M. Vinogradov, L. Vitagliano, R. F. Vitolo, T. T. Voronov, V. G. Kac, Y. Kosmann-Schwarzbach, I. S. Krasil’shchik, I. M. Krichever, A. P. Krishchenko, S. K. Lando, V. V. Lychagin, M. Marvan, V. P. Maslov, A. S. Mishchenko, S. P. Novikov, V. N. Rubtsov, A. V. Samokhin, A. B. Sossinsky, J. Stasheff, D. B. Fuchs, A. Ya. Khelemsky, N. G. Khor’kova, V. N. Chetverikov, and A. S. Schwarz :
“Alexandre Mikhaĭlovich Vinogradov ,”
Usp. Mat. Nauk
75 : 2(452)
(2020 ),
pp. 185–190 .
An English translation was published in Russ. Math. Surv. 75 :2 (2020) .
MR
4081971
article
People
BibTeX
@article {key4081971m,
AUTHOR = {Astashov, A. M. and Astashova, I. V.
and Bocharov, A. V. and Buchstaber,
V. M. and Vassiliev, V. A. and Verbovetsky,
A. M. and Vershik, A. M. and Veselov,
A. P. and Vinogradov, M. M. and Vitagliano,
L. and Vitolo, R. F. and Voronov, Th.
Th. and Kac, V. G. and Kosmann-Schwarzbach,
Y. and Krasil\cprime shchik, I. S. and
Krichever, I. M. and Krishchenko, A.
P. and Lando, S. K. and Lychagin, V.
V. and Marvan, M. and Maslov, V. P.
and Mishchenko, A. S. and Novikov, S.
P. and Rubtsov, V. N. and Samokhin,
A. V. and Sossinsky, A. B. and Stasheff,
J. and Fuchs, D. B. and Khelemsky, A.
Ya. and Khor\cprime kova, N. G. and
Chetverikov, V. N. and Schwarz, A. S.},
TITLE = {Alexandre {M}ikha\u{\i}lovich {V}inogradov},
JOURNAL = {Usp. Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk},
VOLUME = {75},
NUMBER = {2(452)},
YEAR = {2020},
PAGES = {185--190},
DOI = {10.4213/rm9931},
NOTE = {An English translation was published
in \textit{Russ. Math. Surv.} \textbf{75}:2
(2020). MR:4081971.},
ISSN = {0042-1316},
}
A. Schwarz :
Mathematical foundations of quantum field theory .
World Scientific (Hackensack, NJ ),
2020 .
This appears to be based on the author’s Russian-language book with the equivalent title published in 1975 .
MR
4274597
Zbl
06998205
book
BibTeX
@book {key4274597m,
AUTHOR = {Schwarz, Albert},
TITLE = {Mathematical foundations of quantum
field theory},
PUBLISHER = {World Scientific},
ADDRESS = {Hackensack, NJ},
YEAR = {2020},
PAGES = {xlvi + 414},
DOI = {10.1142/11222},
NOTE = {This appears to be based on the author's
Russian-language book with the equivalent
title published in 1975. MR:4274597.
Zbl:06998205.},
ISBN = {9789813278639},
}
A. M. Astashov, I. V. Astashova, A. V. Bocharov, V. M. Buchstaber, V. A. Vassiliev, A. M. Verbovetsky, A. M. Vershik, A. P. Veselov, M. M. Vinogradov, L. Vitagliano, R. F. Vitolo, T. T. Voronov, V. G. Kac, Y. Kosmann-Schwarzbach, I. S. Krasil’shchik, I. M. Krichever, A. P. Krishchenko, S. K. Lando, V. V. Lychagin, M. Marvan, V. P. Maslov, A. S. Mishchenko, S. P. Novikov, V. N. Rubtsov, A. V. Samokhin, A. B. Sossinsky, J. Stasheff, D. B. Fuchs, A. Ya. Khelemsky, N. G. Khor’kova, V. N. Chetverikov, and A. S. Schwarz :
“Alexandre Mikhaĭlovich Vinogradov ,”
Russ. Math. Surv.
75 : 2
(2020 ),
pp. 369–375 .
English translation of Russian original published in Usp. Mat. Nauk 75 :2(452) (2020) .
Zbl
1445.01025
article
People
BibTeX
@article {key1445.01025z,
AUTHOR = {Astashov, A. M. and Astashova, I. V.
and Bocharov, A. V. and Buchstaber,
V. M. and Vassiliev, V. A. and Verbovetsky,
A. M. and Vershik, A. M. and Veselov,
A. P. and Vinogradov, M. M. and Vitagliano,
L. and Vitolo, R. F. and Voronov, Th.
Th. and Kac, V. G. and Kosmann-Schwarzbach,
Y. and Krasil\cprime shchik, I. S. and
Krichever, I. M. and Krishchenko, A.
P. and Lando, S. K. and Lychagin, V.
V. and Marvan, M. and Maslov, V. P.
and Mishchenko, A. S. and Novikov, S.
P. and Rubtsov, V. N. and Samokhin,
A. V. and Sossinsky, A. B. and Stasheff,
J. and Fuchs, D. B. and Khelemsky, A.
Ya. and Khor\cprime kova, N. G. and
Chetverikov, V. N. and Schwarz, A. S.},
TITLE = {Alexandre {M}ikha\u{\i}lovich {V}inogradov},
JOURNAL = {Russ. Math. Surv.},
FJOURNAL = {Russian Mathematical Surveys},
VOLUME = {75},
NUMBER = {2},
YEAR = {2020},
PAGES = {369--375},
DOI = {10.1070/RM9931},
NOTE = {English translation of Russian original
published in \textit{Usp. Mat. Nauk}
\textbf{75}:2(452) (2020). Zbl:1445.01025.},
ISSN = {0036-0279},
}
A. Schwarz :
Scattering in algebraic approach to quantum theory: Associative algebras .
Preprint ,
July 2021 .
ArXiv
2107.08553
techreport
Abstract
BibTeX
The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula) and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state.) An interesting novelty is the consideration of associative algebras over real numbers.
@techreport {key2107.08553a,
AUTHOR = {Schwarz, Albert},
TITLE = {Scattering in algebraic approach to
quantum theory: {A}ssociative algebras},
TYPE = {Preprint},
MONTH = {July},
YEAR = {2021},
PAGES = {20},
URL = {https://arxiv.org/pdf/2107.08553.pdf},
NOTE = {ArXiv:2107.08553.},
}
A. Schwarz :
Geometric and algebraic approaches to quantum theory .
Preprint ,
February 2021 .
ArXiv
2102.09176
techreport
Abstract
BibTeX
We show how to formulate quantum theory taking as a starting point the set of states (geometric approach). We discuss the equations of motion and the formulas for probabilities of physical quantities in this approach. A heuristic proof of decoherence in our setting is used to justify the formulas for probabilities. We show that quantum theory can be obtained from classical theory if we restrict the set of observables. This remark can be used to construct models with any prescribed group of symmetries; one can hope that this construction leads to new interesting models that cannot be build in the conventional framework.
The geometric approach can be used to formulate quantum theory in terms of Jordan algebras, generalizing the algebraic approach to quantum theory. The scattering theory can be formulated in geometric approach.
@techreport {key2102.09176a,
AUTHOR = {Schwarz, Albert},
TITLE = {Geometric and algebraic approaches to
quantum theory},
TYPE = {Preprint},
MONTH = {February},
YEAR = {2021},
PAGES = {22},
URL = {https://arxiv.org/pdf/2102.09176.pdf},
NOTE = {ArXiv:2102.09176.},
}
A. Schwarz :
Scattering in geometric approach to quantum theory .
Technical report ,
July 2021 .
ArXiv
2107.08557
techreport
Abstract
BibTeX
@techreport {key2107.08557a,
AUTHOR = {Schwarz, Albert},
TITLE = {Scattering in geometric approach to
quantum theory},
MONTH = {July},
YEAR = {2021},
PAGES = {14},
URL = {https://arxiv.org/pdf/2107.08557.pdf},
NOTE = {ArXiv:2107.08557.},
}
A. Schwarz :
Scattering theory in algebraic approach: Jordan algebras ,
2021 .
In preparation.
misc
BibTeX
@misc {key84255339,
AUTHOR = {Schwarz, Albert},
TITLE = {Scattering theory in algebraic approach:
Jordan algebras},
YEAR = {2021},
NOTE = {In preparation.},
}