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TMF, 1983, Volume 57, Number 2, Pages 217–231 (Mi tmf2255)  

This article is cited in 1 scientific paper (total in 1 paper)

Group-theoretical derivation of path integrals

M. B. Menskii


Abstract: The dynamics of nonrelativistic particles in the form of a Feynman path integral is derived from group-theo'retical considerations. A group-theoretical approach is used, this making it possible to construct the quantum theory of an elementary particle on the basis of its symmetry group. The quantum properties of the particle arise from the intertwining of two representations of the symmetry group, one of which describes the local properties of the particle, and the other the particle as a whole. This approach is appIied to the generalized Galileo semigroup, which is obtained from the ordinary Galileo group by replacing the translation subgroup by a semigroup of trajectories (parametrized paths). As a result, the propagator of the particle in an external electromagnetic or gauge field is derived in the form of a path integral. The integration measure, including the weight factor $\exp(iS)$, is uniquely determined by the requirement of invariance.

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English version:
Theoretical and Mathematical Physics, 1983, 57:2, 1095–1105

Bibliographic databases:

Received: 09.03.1983

Citation: M. B. Menskii, “Group-theoretical derivation of path integrals”, TMF, 57:2 (1983), 217–231; Theoret. and Math. Phys., 57:2 (1983), 1095–1105

Citation in format AMSBIB
\Bibitem{Men83}
\by M.~B.~Menskii
\paper Group-theoretical derivation of path integrals
\jour TMF
\yr 1983
\vol 57
\issue 2
\pages 217--231
\mathnet{http://mi.mathnet.ru/tmf2255}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=734885}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 57
\issue 2
\pages 1095--1105
\crossref{https://doi.org/10.1007/BF01018652}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983SX71000005}


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  • http://mi.mathnet.ru/eng/tmf/v57/i2/p217

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. B. Menskii, “A group theory derivation of the relativistic path integral and the “history-string” dynamics”, Theoret. and Math. Phys., 173:3 (2012), 1668–1686  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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