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TMF, 1994, Volume 100, Number 1, Pages 3–13 (Mi tmf1623)  

This article is cited in 5 scientific papers (total in 5 papers)

Transformations of Feynman integral under some nonlinear transformations of the phase space

O. G. Smolyanova, M. O. Smolyanova

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The Feynman measure is defined as a linear continuous functional on a space of test functions (which is introduced in paper), having a given Fourier transformation. Both the case of a positevely defined and the case of an arbitrary correlation operators are considered (the last one is related to the so-called symplectic, or Hamiltonian, Feynman measure). The Feynman integral is the value of the Feynman measure on a function (from the space of test functions). The transformations of the Feynman measure under the nonlinear transformations of the phase space which are included by both the translations along vector fields and along the integral curves of vector fields are described. The formulae that are similar to Cameron–Martin, Girsanov–Maruyama and Ramer formulae (from the theory of Gaussian measures) are obtained. The results can be considered as formulae of change of variables in the Feynman integral.

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English version:
Theoretical and Mathematical Physics, 1994, 100:1, 803–810

Bibliographic databases:

Received: 05.04.1993

Citation: O. G. Smolyanov, M. O. Smolyanova, “Transformations of Feynman integral under some nonlinear transformations of the phase space”, TMF, 100:1 (1994), 3–13; Theoret. and Math. Phys., 100:1 (1994), 803–810

Citation in format AMSBIB
\Bibitem{SmoSmo94}
\by O.~G.~Smolyanov, M.~O.~Smolyanova
\paper Transformations of Feynman integral under some nonlinear transformations of the phase space
\jour TMF
\yr 1994
\vol 100
\issue 1
\pages 3--13
\mathnet{http://mi.mathnet.ru/tmf1623}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1305786}
\zmath{https://zbmath.org/?q=an:1041.81549}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 100
\issue 1
\pages 803--810
\crossref{https://doi.org/10.1007/BF01017317}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994QC09900001}


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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. O. G. Smolyanov, A. Trumen, “Change of variable formulas for Feynman pseudomeasures”, Theoret. and Math. Phys., 119:3 (1999), 677–686  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Smolyanov, OG, “Hamiltonian Feynman path integrals via the Chernoff formula”, Journal of Mathematical Physics, 43:10 (2002), 5161  crossref  mathscinet  zmath  adsnasa  isi
    3. “Introduction”, Mathematical Theory of Feynman Path Integrals: An Introduction, 523 (2008), 1  crossref  mathscinet  isi
    4. Fedorov A.K., Yurchenko S.O., “Simplekticheskie tomogrammy v predstavlenii feinmanovskimi integralami po traektoriyam”, Vestnik moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N.E. Baumana. seriya: estestvennye nauki, 2012, no. 2, 29–37  elib
    5. Orlov Yu.N. Sakbaev V.Zh. Smolyanov O.G., “Feynman Formulas For Nonlinear Evolution Equations”, Dokl. Math., 96:3 (2017), 574–577  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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