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Reviews of topical problems


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.

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Fulltext is also available at DOI: 10.1070/PU1980v023n11ABEH005062
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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Îðèãèíàë: Áåðåçèí Ô À «Êîíòèíóàëüíûé èíòåãðàë ïî òðàåêòîðèÿì â ôàçîâîì ïðîñòðàíñòâå» ÓÔÍ 132 497–548 (1980); DOI: 10.3367/UFNr.0132.198011d.0497

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