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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 93, Number 1, Pages 17–31 (Mi tmf5727)  
This article is cited in 2 scientific papers (total in 2 papers)

Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations

S. N. Storchak

Institute for High Energy Physics
Full-text PDF (1369 kB) Citations (2)
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Abstract: It is shown that one can generalize the procedure of a stochastic change of time to random processes associated with fourth-order differential equations. Using this procedure, and also the obtained analog of the Girsanov–Cameron–Martin formula, we derive a formula for transforming a path integral (as an integral with respect to a quasimeasure) under path reparametrization. By means of the reparametrization formula and the formula for transforming the path integral under a homogeneous point transformation of the phase space we obtain an integral relation, expressed in terms of symbols of path integrals, between the Green's functions of two quantum-mechanical problems associated with fourth-order differential equations.
Received: 10.01.1992
English version:
Theoretical and Mathematical Physics, 1992, Volume 93, Issue 1, Pages 1091–1100
DOI: https://doi.org/10.1007/BF01016466
Bibliographic databases:
Language: Russian
Citation: S. N. Storchak, “Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations”, TMF, 93:1 (1992), 17–31; Theoret. and Math. Phys., 93:1 (1992), 1091–1100
Citation in format AMSBIB
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\by S.~N.~Storchak
\paper Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations
\jour TMF
\yr 1992
\vol 93
\issue 1
\pages 17--31
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1226207}
\zmath{https://zbmath.org/?q=an:0786.60123}
\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 93
\issue 1
\pages 1091--1100
\crossref{https://doi.org/10.1007/BF01016466}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992LF86000002}
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  • https://www.mathnet.ru/eng/tmf5727
  • https://www.mathnet.ru/eng/tmf/v93/i1/p17
    • This publication is cited in the following 2 articles:
    1. S. N. Storchak, “Reonomic homogenious contact transformations and path reparametrization in path integrals over quasi-measures”, Theoret. and Math. Phys., 111:2 (1997), 576–582  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. N. Storchak, “Nonstationary generalized Duru–Kleinert transformation of path integrals for systems of differential equations in the one-dimensional space”, Theoret. and Math. Phys., 109:1 (1996), 1260–1268  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:44
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