RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (942 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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} 

• http://mi.mathnet.ru/eng/tmf2255
• http://mi.mathnet.ru/eng/tmf/v57/i2/p217

 SHARE:

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
•  Number of views: This page: 327 Full text: 146 References: 34 First page: 1