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TMF, 1984, Volume 60, Number 3, Pages 344–355 (Mi tmf5349)  

This article is cited in 2 scientific papers (total in 3 papers)

Trace formula in general Hamiltonian mechanics

V. S. Buslaev, E. A. Nalimova


Abstract: The variational equation corresponding to a fixed interval of the trajectory of a Bamiltonian system of classical dynamics generates a linear canonical differential operator. If a connection consistent with the sympleetic structure is defined on the tangent bundle of the phase space, it is possible to introduce a regularized determinant of such an operator. The trace formula expresses this determinant in terms of the Jacobian of a transformation that is determined by the motion of the classical system and acts on a space with dimension equal to the number of degrees of freedom. A connection between the relations that are obtained and the semielassical asymptotic behavior for the functional integral that describes the dynamics of the corresponding quantum system is noted.

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English version:
Theoretical and Mathematical Physics, 1984, 60:3, 863–871

Bibliographic databases:

Received: 14.10.1983

Citation: V. S. Buslaev, E. A. Nalimova, “Trace formula in general Hamiltonian mechanics”, TMF, 60:3 (1984), 344–355; Theoret. and Math. Phys., 60:3 (1984), 863–871

Citation in format AMSBIB
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\by V.~S.~Buslaev, E.~A.~Nalimova
\paper Trace formula in general Hamiltonian mechanics
\jour TMF
\yr 1984
\vol 60
\issue 3
\pages 344--355
\mathnet{http://mi.mathnet.ru/tmf5349}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=768163}
\zmath{https://zbmath.org/?q=an:0598.70018}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 60
\issue 3
\pages 863--871
\crossref{https://doi.org/10.1007/BF01017887}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AEF5000002}


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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. V. S. Buslaev, E. A. Nalimova, “Trace formula in Lagrangian mechanics”, Theoret. and Math. Phys., 61:1 (1984), 989–997  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. M. Vorob'ev, “Hamiltonian structures of the first variation equations and symplectic connections”, Sb. Math., 191:4 (2000), 477–502  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. M. Babich, A. M. Budylin, L. A. Dmitrieva, A. I. Komech, S. B. Levin, M. V. Perel', E. A. Rybakina, V. V. Sukhanov, A. A. Fedotov, “On the mathematical work of Vladimir Savel'evich Buslaev”, St. Petersburg Math. J., 25:2 (2014), 151–174  mathnet  crossref  mathscinet  zmath  isi  elib
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