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 TMF, 1977, Volume 30, Number 2, Pages 159–167 (Mi tmf2778)

Feynman path integrals on nonlinear phase space

A. L. Alimov

Abstract: Definition of Feynman continual integral in Hamiltonian form on cotangential fibering of the Riemann space $M$ is given. Representation of the solution of parabolic type equation on $M$ in the form of the continual integral is established. It is shown that at the Feynman quantization (when operators are put into correspondence to functionals by means of continual integral) function of the functional of the form $\int\limits_0^1 Hd\sigma$ corresponds to the function of the operator $\hat H$. Extension of this result to the case of functions. of noncommuting operators is given.

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English version:
Theoretical and Mathematical Physics, 1977, 30:2, 100–106

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Citation: A. L. Alimov, “Feynman path integrals on nonlinear phase space”, TMF, 30:2 (1977), 159–167; Theoret. and Math. Phys., 30:2 (1977), 100–106

Citation in format AMSBIB
\Bibitem{Ali77} \by A.~L.~Alimov \paper Feynman path integrals on~nonlinear phase space \jour TMF \yr 1977 \vol 30 \issue 2 \pages 159--167 \mathnet{http://mi.mathnet.ru/tmf2778} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=456122} \transl \jour Theoret. and Math. Phys. \yr 1977 \vol 30 \issue 2 \pages 100--106 \crossref{https://doi.org/10.1007/BF01029281} 

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This publication is cited in the following articles:
1. M. V. Karasev, V. P. Maslov, “Asymptotic and geometric quantization”, Russian Math. Surveys, 39:6 (1984), 133–205
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