M. F. Atiyah, N. J. Hitchin, and I. M. Singer :
“Deformations of instantons Proc. Nat. Acad. Sci. U.S.A.
74 : 7
(July 1977 ),
pp. 2662–2663 .
MR
458424 Zbl
0356.58011 article
Abstract
People
BibTeX
@article {key458424m,
AUTHOR = {Atiyah, M. F. and Hitchin, N. J. and
Singer, I. M.},
TITLE = {Deformations of instantons},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {74},
NUMBER = {7},
MONTH = {July},
YEAR = {1977},
PAGES = {2662--2663},
URL = {http://www.pnas.org/content/74/7/2662.short},
NOTE = {MR:458424. Zbl:0356.58011.},
ISSN = {0027-8424},
}
M. F. Atiyah, N. J. Hitchin, V. G. Drinfel’d, and Yu. I. Manin :
“Construction of instantons Phys. Lett. A
65 : 3
(1978 ),
pp. 185–187 .
MR
598562 article
Abstract
People
BibTeX
@article {key598562m,
AUTHOR = {Atiyah, M. F. and Hitchin, N. J. and
Drinfel{\cprime}d, V. G. and Manin,
Yu. I.},
TITLE = {Construction of instantons},
JOURNAL = {Phys. Lett. A},
FJOURNAL = {Physics Letters A},
VOLUME = {65},
NUMBER = {3},
YEAR = {1978},
PAGES = {185--187},
DOI = {10.1016/0375-9601(78)90141-X},
NOTE = {MR:598562.},
ISSN = {0031-9163},
}
M. F. Atiyah, N. J. Hitchin, and I. M. Singer :
“Self-duality in four-dimensional Riemannian geometry Proc. Roy. Soc. London Ser. A
362 : 1711
(September 1978 ),
pp. 425–461 .
MR
506229 Zbl
0389.53011 article
Abstract
People
BibTeX
@article {key506229m,
AUTHOR = {Atiyah, M. F. and Hitchin, N. J. and
Singer, I. M.},
TITLE = {Self-duality in four-dimensional {R}iemannian
geometry},
JOURNAL = {Proc. Roy. Soc. London Ser. A},
FJOURNAL = {Proceedings of the Royal Society. London.
Series A. Mathematical and Physical
Sciences},
VOLUME = {362},
NUMBER = {1711},
MONTH = {September},
YEAR = {1978},
PAGES = {425--461},
DOI = {10.1098/rspa.1978.0143},
NOTE = {MR:506229. Zbl:0389.53011.},
ISSN = {0080-4630},
}
M. F. Atiyah :
“The moment map in symplectic geometry ,”
pp. 43–51
in
Global Riemannian geometry
(Durham University, UK, July 1983 ).
Edited by T. Willmore and N. J. Hitchin .
Mathematics and its Applications .
Ellis Horwood (Chichester, UK ),
1984 .
MR
757204 Zbl
0615.53023 incollection
People
BibTeX
@incollection {key757204m,
AUTHOR = {Atiyah, M. F.},
TITLE = {The moment map in symplectic geometry},
BOOKTITLE = {Global {R}iemannian geometry},
EDITOR = {Thomas Willmore and Nigel J. Hitchin},
SERIES = {Mathematics and its Applications},
PUBLISHER = {Ellis Horwood},
ADDRESS = {Chichester, UK},
YEAR = {1984},
PAGES = {43--51},
NOTE = {(Durham University, UK, July 1983).
MR:757204. Zbl:0615.53023.},
ISBN = {9780470200179},
}
M. F. Atiyah :
“The Yang–Mills equations and the structure of 4-manifolds ,”
pp. 11–17
in
Global Riemannian geometry
(Durham University, UK, July 1983 ).
Edited by T. Willmore and N. J. Hitchin .
Series in Mathematics and its Applications .
Ellis Horwood (Chichester, UK ),
1984 .
MR
757200 Zbl
0614.57007 incollection
People
BibTeX
@incollection {key757200m,
AUTHOR = {Atiyah, M. F.},
TITLE = {The {Y}ang--{M}ills equations and the
structure of 4-manifolds},
BOOKTITLE = {Global {R}iemannian geometry},
EDITOR = {Thomas Willmore and Nigel J. Hitchin},
SERIES = {Series in Mathematics and its Applications},
PUBLISHER = {Ellis Horwood},
ADDRESS = {Chichester, UK},
YEAR = {1984},
PAGES = {11--17},
NOTE = {(Durham University, UK, July 1983).
MR:757200. Zbl:0614.57007.},
ISBN = {9780470200179},
}
M. F. Atiyah and N. J. Hitchin :
“Low energy scattering of nonabelian monopoles Phys. Lett. A
107 : 1
(1985 ),
pp. 21–25 .
MR
778313 Zbl
1177.53069 article
Abstract
People
BibTeX
@article {key778313m,
AUTHOR = {Atiyah, M. F. and Hitchin, N. J.},
TITLE = {Low energy scattering of nonabelian
monopoles},
JOURNAL = {Phys. Lett. A},
FJOURNAL = {Physics Letters A},
VOLUME = {107},
NUMBER = {1},
YEAR = {1985},
PAGES = {21--25},
DOI = {10.1016/0375-9601(85)90238-5},
NOTE = {MR:778313. Zbl:1177.53069.},
ISSN = {0375-9601},
}
M. Atiyah, N. J. Hitchin, J. T. Stuart, and M. Tabor :
“Low-energy scattering of nonabelian magnetic monopoles [and discussion] Philos. Trans. Roy. Soc. London Ser. A
315 : 1533
(1985 ),
pp. 459–469 .
MR
836746 article
Abstract
People
BibTeX
The Bogomolny equations represent static configurations of magnetic monopoles, for some non-Abelian group such as \( \mathit{SU}(2) \) . Geodesic motion on this configuration space represents slowly moving interacting monopoles. Geometric information on this space can then be used to investigate the scattering of monopoles. The results show surprising features, including a 90 degrees scattering and the conversion of angular momentum into electric charge.
@article {key836746m,
AUTHOR = {Atiyah, Michael and Hitchin, N. J. and
Stuart, J. T. and Tabor, M.},
TITLE = {Low-energy scattering of nonabelian
magnetic monopoles [and discussion]},
JOURNAL = {Philos. Trans. Roy. Soc. London Ser.
A},
FJOURNAL = {Philosophical Transactions of the Royal
Society A: Mathematical, Physical \&
Engineering Sciences},
VOLUME = {315},
NUMBER = {1533},
YEAR = {1985},
PAGES = {459--469},
DOI = {10.1098/rsta.1985.0052},
NOTE = {MR:836746.},
ISSN = {0080-4614},
}
M. Atiyah and N. Hitchin :
The geometry and dynamics of magnetic monopoles .
M. B. Porter Lectures .
Princeton University Press ,
1988 .
Russian translation published as Geometriya i dinamika magnitnykh monopolei (1991)
MR
934202 Zbl
0671.53001 book
People
BibTeX
@book {key934202m,
AUTHOR = {Atiyah, Michael and Hitchin, Nigel},
TITLE = {The geometry and dynamics of magnetic
monopoles},
SERIES = {M.~B. Porter Lectures},
PUBLISHER = {Princeton University Press},
YEAR = {1988},
PAGES = {viii+134},
NOTE = {Russian translation published as \textit{Geometriya
i dinamika magnitnykh monopolei} (1991).
MR:934202. Zbl:0671.53001.},
ISBN = {9780691084800},
}
M. Atiyah and N. Khitchin :
Geometriya i dinamika magnitnykh monopolei
[The geometry and dynamics of magnetic monopoles ].
Mir (Moscow ),
1991 .
Russian translation of The geometry and dynamics of magnetic monopoles (1988)
MR
1137269 Zbl
0754.53003 book
People
BibTeX
@book {key1137269m,
AUTHOR = {Atiyah, M. and Khitchin, N.},
TITLE = {Geometriya i dinamika magnitnykh monopolei
[The geometry and dynamics of magnetic
monopoles]},
PUBLISHER = {Mir},
ADDRESS = {Moscow},
YEAR = {1991},
PAGES = {150},
NOTE = {Russian translation of \textit{The geometry
and dynamics of magnetic monopoles}
(1988). MR:1137269. Zbl:0754.53003.},
ISBN = {9785030017945},
}
M. Atiyah :
“Mathematical work of Nigel Hitchin 11–16
in
The many facets of geometry .
Edited by O. García-Prada, J. P. Bourguignon, and S. Salamon .
Oxford University Press (New York ),
2010 .
MR
2681683 Zbl
1206.01039 incollection
Abstract
People
BibTeX
This chapter reviews selected topics covered in Nigel Hitchin’s papers. These include his introduction of the spectral curve of a magnetic monopole, the introduction by Nigel of “Higgs bundles” in 1987, and the work of Nigel and his collaborators on the hyperkähler quotient construction.
@incollection {key2681683m,
AUTHOR = {Atiyah, Michael},
TITLE = {Mathematical work of {N}igel {H}itchin},
BOOKTITLE = {The many facets of geometry},
EDITOR = {Oscar Garc\'ia-Prada and Jean Pierre
Bourguignon and Simon Salamon},
PUBLISHER = {Oxford University Press},
ADDRESS = {New York},
YEAR = {2010},
PAGES = {11--16},
DOI = {10.1093/acprof:oso/9780199534920.003.0002},
NOTE = {MR:2681683. Zbl:1206.01039.},
ISBN = {9780199534920},
}
M. Atiyah, R. Dijkgraaf, and N. Hitchin :
“Geometry and physics Philos. Trans. R. Soc. Lond. Ser. A
368 : 1914
(2010 ),
pp. 913–926 .
MR
2587923 Zbl
pre05764159 article
Abstract
People
BibTeX
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology.
@article {key2587923m,
AUTHOR = {Atiyah, Michael and Dijkgraaf, Robbert
and Hitchin, Nigel},
TITLE = {Geometry and physics},
JOURNAL = {Philos. Trans. R. Soc. Lond. Ser. A},
FJOURNAL = {Philosophical Transactions of the Royal
Society A: Mathematical, Physical \&
Engineering Sciences},
VOLUME = {368},
NUMBER = {1914},
YEAR = {2010},
PAGES = {913--926},
DOI = {10.1098/rsta.2009.0227},
NOTE = {MR:2587923. Zbl:pre05764159.},
ISSN = {1364-503X},
}
