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)

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%0 Journal Article
%T Feynman path integrals in a phase space
%A F. A. Berezin
%I Physics-Uspekhi
%D 1980
%J Phys. Usp.
%V 23
%N 11
%P 763-788
%U https://ufn.ru/en/articles/1980/11/d/
%U https://doi.org/10.1070/PU1980v023n11ABEH005062

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