J. R. Klauder and I. Daubechies :
“Measures for path integrals Phys. Rev. Lett.
48 : 3
(1982 ),
pp. 117–120 .
MR
639863 article
Abstract
People
BibTeX
@article {key639863m,
AUTHOR = {Klauder, John R. and Daubechies, Ingrid},
TITLE = {Measures for path integrals},
JOURNAL = {Phys. Rev. Lett.},
FJOURNAL = {Physical Review Letters},
VOLUME = {48},
NUMBER = {3},
YEAR = {1982},
PAGES = {117--120},
DOI = {10.1103/PhysRevLett.48.117},
NOTE = {MR:639863.},
ISSN = {0031-9007},
}
I. Daubechies and J. R. Klauder :
“Constructing measures for path integrals J. Math. Phys.
23 : 10
(1982 ),
pp. 1806–1822 .
MR
676020 article
Abstract
People
BibTeX
@article {key676020m,
AUTHOR = {Daubechies, Ingrid and Klauder, John
R.},
TITLE = {Constructing measures for path integrals},
JOURNAL = {J. Math. Phys.},
FJOURNAL = {Journal of Mathematical Physics},
VOLUME = {23},
NUMBER = {10},
YEAR = {1982},
PAGES = {1806--1822},
DOI = {10.1063/1.525234},
NOTE = {MR:676020.},
ISSN = {0022-2488},
}
J. R. Klauder and I. Daubechies :
“Wiener measures for quantum mechanical path integrals 245–247
in
Stochastic processes in quantum theory and statistical physics
(Marseille, France, 29 June–4 July 1981 ).
Edited by S. Albeverio, P. Combe, and M. Sirugue-Collin .
Lecture Notes in Physics 173 .
Springer (Berlin ),
1982 .
Zbl
0496.60066 incollection
Abstract
People
BibTeX
Our purpose here is to show that it is possible to represent certain quantum mechanial evolution operators by path integrals with mathematically well-defined measures. For the Hamiltonians we consider here, this measure will be a Wiener measure on phase space. To achieve this goal we exploit the overcompleteness of the coherent states.
@incollection {key0496.60066z,
AUTHOR = {Klauder, John R. and Daubechies, Ingrid},
TITLE = {Wiener measures for quantum mechanical
path integrals},
BOOKTITLE = {Stochastic processes in quantum theory
and statistical physics},
EDITOR = {Albeverio, S. and Combe, P. and Sirugue-Collin,
M.},
SERIES = {Lecture Notes in Physics},
NUMBER = {173},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
PAGES = {245--247},
DOI = {10.1007/3-540-11956-6_123},
NOTE = {(Marseille, France, 29 June--4 July
1981). Zbl:0496.60066.},
ISSN = {0075-8450},
ISBN = {9783540119562},
}
I. Daubechies and J. R. Klauder :
“Measures for more quadratic path integrals Lett. Math. Phys.
7 : 3
(1983 ),
pp. 229–234 .
MR
706212 Zbl
0521.60078 article
Abstract
People
BibTeX
@article {key706212m,
AUTHOR = {Daubechies, Ingrid and Klauder, John
R.},
TITLE = {Measures for more quadratic path integrals},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics. A Journal
for the Rapid Dissemination of Short
Contributions in the Field of Mathematical
Physics},
VOLUME = {7},
NUMBER = {3},
YEAR = {1983},
PAGES = {229--234},
DOI = {10.1007/BF00400438},
NOTE = {MR:706212. Zbl:0521.60078.},
ISSN = {0377-9017},
}
I. Daubechies and J. R. Klauder :
“Quantum-mechanical path integrals with Wiener measure for all polynomials Hamiltonians Phys. Rev. Lett.
52 : 14
(1984 ),
pp. 1161–1164 .
Part II was published in J. Math. Phys 26 (1985)
MR
736821 article
Abstract
People
BibTeX
We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well defined path integrals involving Wiener measure on phase space, as the diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian.
@article {key736821m,
AUTHOR = {Daubechies, Ingrid and Klauder, John
R.},
TITLE = {Quantum-mechanical path integrals with
{W}iener measure for all polynomials
{H}amiltonians},
JOURNAL = {Phys. Rev. Lett.},
FJOURNAL = {Physical Review Letters},
VOLUME = {52},
NUMBER = {14},
YEAR = {1984},
PAGES = {1161--1164},
DOI = {10.1103/PhysRevLett.52.1161},
NOTE = {Part II was published in \textit{J.
Math. Phys} \textbf{26} (1985). MR:736821.},
ISSN = {0031-9007},
}
I. Daubechies and J. R. Klauder :
“Quantum-mechanical path integrals with Wiener measure for all polynomials Hamiltonians, II J. Math. Phys.
26
(1985 ),
pp. 2239–2256 .
Part I was published in Phys. Rev. Lett. 52 :14 (1984)
MR
801118 Zbl
0979.81517 article
Abstract
People
BibTeX
The coherent-state representation of quantum-mechanical propagators as well-defined phase-space path integrals involving Wiener measure on continuous phase-space paths in the limit that the diffusion constant diverges is formulated and proved. This construction covers a wide class of self-adjoint Hamiltonians, including all those which are polynomials in the Heisenberg operators; in fact, this method also applies to maximal symmetric Hamiltonians that do not possess a self-adjoint extension. This construction also leads to a natural covariance of the path integral under canonical transformations. An entirely parallel discussion for spin variables leads to the representation of the propagator for an arbitrary spin-operator Hamiltonian as well-defined path integrals involving Wiener measure on the unit sphere, again in the limit that the diffusion constant diverges.
@article {key801118m,
AUTHOR = {Daubechies, Ingrid and Klauder, John
R.},
TITLE = {Quantum-mechanical path integrals with
{W}iener measure for all polynomials
{H}amiltonians, {II}},
JOURNAL = {J. Math. Phys.},
FJOURNAL = {Journal of Mathematical Physics},
VOLUME = {26},
YEAR = {1985},
PAGES = {2239--2256},
DOI = {10.1063/1.526803},
NOTE = {Part I was published in \textit{Phys.
Rev. Lett.} \textbf{52}:14 (1984). MR:801118.
Zbl:0979.81517.},
ISSN = {0022-2488},
}
I. Daubechies and J. R. Klauder :
“True measures for real time path integrals ,”
pp. 425–432
in
Path integrals from meV to MeV
(Bielefeld, Germany, 5–9 August 1985 ).
Edited by M. C. Gutzwiller, A. Inomata, J. R. Klauder, and L. Streit .
Bielefeld Encounters in Physics and Mathematics 7 .
World Scientific (Singapore ),
1986 .
MR
859247 incollection
People
BibTeX
@incollection {key859247m,
AUTHOR = {Daubechies, I. and Klauder, J. R.},
TITLE = {True measures for real time path integrals},
BOOKTITLE = {Path integrals from me{V} to {M}e{V}},
EDITOR = {Gutzwiller, M. C. and Inomata, A. and
Klauder, J. R. and Streit, L.},
SERIES = {Bielefeld Encounters in Physics and
Mathematics},
NUMBER = {7},
PUBLISHER = {World Scientific},
ADDRESS = {Singapore},
YEAR = {1986},
PAGES = {425--432},
NOTE = {(Bielefeld, Germany, 5--9 August 1985).
MR:859247.},
ISBN = {9789971500665},
}
I. Daubechies, J. R. Klauder, and T. Paul :
“Wiener measures for path integrals with affine kinematic variables J. Math. Phys.
28
(1987 ),
pp. 85–102 .
Zbl
0615.58008 article
Abstract
People
BibTeX
The results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator \( \exp(-iTH) \) can be written as a well-defined Wiener integral, involving Wiener measure on the Lobachevsky half-plane, in the limit that the diffusion constant diverges. This approach works for a wide class of Hamiltonians, including, e.g.,
\[ -\frac{d^2}{dx^2}+V(x) \]
on \( L^2(\mathbb{R}_+) \) , with \( V \) sufficiently singular at \( x=0 \) .
@article {key0615.58008z,
AUTHOR = {Daubechies, Ingrid and Klauder, John
R. and Paul, Thierry},
TITLE = {Wiener measures for path integrals with
affine kinematic variables},
JOURNAL = {J. Math. Phys.},
FJOURNAL = {Journal of Mathematical Physics},
VOLUME = {28},
YEAR = {1987},
PAGES = {85--102},
DOI = {10.1063/1.527812},
NOTE = {Zbl:0615.58008.},
ISSN = {0022-2488},
}
I. Daubechies and J. R. Klauder :
“Squeezed states and path integrals 247–259
in
Workshop on squeezed states and uncertainty relations
(College Park, MD, 28–30 March 1991 ).
Edited by D. Han, Y. S. Kim, and W. W. Zachary .
NASA Conference Publications 3135 .
NASA (Washington, DC ),
1992 .
incollection
Abstract
People
BibTeX
The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.
@incollection {key33962884,
AUTHOR = {Daubechies, I. and Klauder, J. R.},
TITLE = {Squeezed states and path integrals},
BOOKTITLE = {Workshop on squeezed states and uncertainty
relations},
EDITOR = {Han, D. and Kim, Y. S. and Zachary,
W. W.},
SERIES = {NASA Conference Publications},
NUMBER = {3135},
PUBLISHER = {NASA},
ADDRESS = {Washington, DC},
YEAR = {1992},
PAGES = {247--259},
URL = {https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920012830.pdf},
NOTE = {(College Park, MD, 28--30 March 1991).},
}
I. Daubechies :
“Orthonormal bases of coherent states: The canonical case and the \( ax+b \) -group ,”
pp. 103–117
in
Coherent states: Past, present, and future
(Oak Ridge, TN, 14–17 June 1993 ).
Edited by D. H. Feng, J. R. Klauder, and M. R. Strayer .
World Scientific (Singapore ),
1994 .
incollection
Abstract
People
BibTeX
This review article tells the story of the search for convenient bases with good phase space localization properties. It describes some useful bases that deserve to be known by a wider community. In particular, some of these bases may well turn out to be good and versatile tools in frameworks where other coherent state families are now used for computations.
@incollection {key30126289,
AUTHOR = {Daubechies, I.},
TITLE = {Orthonormal bases of coherent states:
{T}he canonical case and the \$ax+b\$-group},
BOOKTITLE = {Coherent states: {P}ast, present, and
future},
EDITOR = {Feng, D. H. and Klauder, J. R. and Strayer,
M. R.},
PUBLISHER = {World Scientific},
ADDRESS = {Singapore},
YEAR = {1994},
PAGES = {103--117},
NOTE = {(Oak Ridge, TN, 14--17 June 1993).},
ISBN = {9789814503839},
}
I. Daubechies :
“Affine coherent states and wavelets ,”
pp. 35–42
in
On Klauder’s path: A field trip: Essays in honor of John R. Klauder .
Edited by G. G. Emch, G. C. Hegerfeldt, and L. Streit .
World Scientific (Singapore ),
1994 .
MR
1350560 Zbl
0942.81559 incollection
Abstract
People
BibTeX
@incollection {key1350560m,
AUTHOR = {Daubechies, Ingrid},
TITLE = {Affine coherent states and wavelets},
BOOKTITLE = {On {K}lauder's path: {A} field trip:
{E}ssays in honor of {J}ohn {R}. {K}lauder},
EDITOR = {Emch, Gerard G. and Hegerfeldt, G. C.
and Streit, Ludwig},
PUBLISHER = {World Scientific},
ADDRESS = {Singapore},
YEAR = {1994},
PAGES = {35--42},
NOTE = {MR:1350560. Zbl:0942.81559.},
ISBN = {9789810216870},
}
