Feynman path integrals in a phase space

Feynman path integrals in a phase space are analyzed in detail. The analysis is based on the theory of operator symbols, in contrast with the traditional approach based on the direct use of canonical commutation relations. Particular attention is paid to the Weyl and Wick symbols, which are the most important in applications. The set of paths on which the integral is concentrated is studied. It is found that these paths are always discontinuous. This discontinuity is responsible for errors in certain papers on path integrals in a phase space. The most important properties of the Weyl and Wick symbols are reviewed.

PACS: 03.65.Fd
DOI: 10.1070/PU1980v023n11ABEH005062
URL: https://ufn.ru/en/articles/1980/11/d/
Citation: Berezin F A "Feynman path integrals in a phase space" Sov. Phys. Usp. 23 763–788 (1980)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Березин Ф А «Континуальный интеграл по траекториям в фазовом пространстве» УФН 132 497–548 (1980); DOI: 10.3367/UFNr.0132.198011d.0497

Cited by (137) Similar articles (20) ↓

V.I. Tatarskii “The Wigner representation of quantum mechanics” Sov. Phys. Usp. 26 311–327 (1983)
A.M. Perelomov “Generalized coherent states and some of their applications” Sov. Phys. Usp. 20 703–720 (1977)
D.I. Blokhintsev, B.M. Barbashov “Use of Functional Integrals in Quantum Mechanics and Field Theory” Sov. Phys. Usp. 15 193–204 (1972)
P.V. Elyutin “The quantum chaos problem” Sov. Phys. Usp. 31 597–622 (1988)
L.E. Gendenshtein, I.V. Krive “Supersymmetry in quantum mechanics” Sov. Phys. Usp. 28 645–666 (1985)
F.V. Bunkin, A.E. Kazakov, M.V. Fedorov “Interaction of intense optical radiation with free electrons (nonrelativistic case)” Sov. Phys. Usp. 15 416–435 (1973)
Ya.A. Smorodinskii, L.A. Shelepin “Clebsch-Gordan coefficients, viewed from different sides” Sov. Phys. Usp. 15 1–24 (1972)
Ya.A. Smorodinskii, A.L. Shelepin, L.A. Shelepin “Groups and probabilities at the foundations of quantum mechanics” Sov. Phys. Usp. 35 (12) 1005–1051 (1992)
A.V. Turbiner “The eigenvalue spectrum in quantum mechanics and the nonlinearization procedure” Sov. Phys. Usp. 27 668–694 (1984)
L.D. Faddeev, V.N. Popov “Covariant quantization of the gravitational field” Sov. Phys. Usp. 16 777–788 (1974)
A.A. Migdal “Stochastic quantization of field theory” Sov. Phys. Usp. 29 389–411 (1986)
A.Yu. Morozov “Anomalies in gauge theories” Sov. Phys. Usp. 29 993–1039 (1986)
D.F. Smirnov, A.S. Troshin “New phenomena in quantum optics: photon antibunching, sub-Poisson photon statistics, and squeezed states” Sov. Phys. Usp. 30 851–874 (1987)
V.V. Babikov “The phase-function method in quantum mechanics” Sov. Phys. Usp. 10 271–284 (1967)
D.N. Zubarev “Double-time Green functions in statistical physics” Sov. Phys. Usp. 3 320–345 (1960)
A.I. Morosov, A.S. Sigov “Surface spin-flop transition in an antiferromagnet” Phys. Usp. 53 677–689 (2010)
P.S. Landa, N.A. Miskinova, Yu.V. Ponomarev “lonization waves in low-temperature plasmas” Sov. Phys. Usp. 23 813–834 (1980)
R.N. Gurzhi, A.I. Kopeliovich “Low-temperature electrical conductivity of pure metals” Sov. Phys. Usp. 24 17–41 (1981)
A.V. Kolpakov, V.A. Bushuev, R.N. Kuz’min “Dielectric permittivity in the x-ray region” Sov. Phys. Usp. 21 959–977 (1978)
V.N. Dudorov, V.V. Randoshkin, R.V. Telesnin “Synthesis and physical properties of single-crystal films of rare-earth iron garnets” Sov. Phys. Usp. 20 505–527 (1977)

The list is formed automatically.