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 TMF, 1979, Volume 40, Number 1, Pages 51–63 (Mi tmf2802)

Path integrals and ordering of operators

L. F. Blazhievskii

Abstract: A method, not based on finite-multiplicity approximations, is proposed for constructing the Feynman path integral for a particle in a curved space whose geometry is defined by the kinetic energy. For the example of a system with the Hamiltonian $H=f^2(x)p^2$ (and some other systems) it is shown that the path integral can be obtained by a change of the variables of integration from a Gaussian functional integral, and this then makes it possible to associate the function $H$ uniquely with an operator. The procedure for constructing the operator corresponding to a classical function of the coordinates and the momenta, for given form of the Hamiltonian, is also considered.

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English version:
Theoretical and Mathematical Physics, 1979, 40:1, 596–604

Bibliographic databases:

Citation: L. F. Blazhievskii, “Path integrals and ordering of operators”, TMF, 40:1 (1979), 51–63; Theoret. and Math. Phys., 40:1 (1979), 596–604

Citation in format AMSBIB
\Bibitem{Bla79} \by L.~F.~Blazhievskii \paper Path integrals and ordering of operators \jour TMF \yr 1979 \vol 40 \issue 1 \pages 51--63 \mathnet{http://mi.mathnet.ru/tmf2802} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=543979} \zmath{https://zbmath.org/?q=an:0442.28017} \transl \jour Theoret. and Math. Phys. \yr 1979 \vol 40 \issue 1 \pages 596--604 \crossref{https://doi.org/10.1007/BF01019242} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JG40800006} 

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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. L. F. Blazhievskii, “Path integrals in configuration space in weakly relativistic many-body theory”, Theoret. and Math. Phys., 66:3 (1986), 270–278
2. S. N. Storchak, “Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations”, Theoret. and Math. Phys., 93:1 (1992), 1091–1100
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