Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 344-355
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V. S. Buslaev; E. A. Nalimova. Trace formula in general Hamiltonian mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 344-355. http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a1/
@article{TMF_1984_60_3_a1,
author = {V. S. Buslaev and E. A. Nalimova},
title = {Trace formula in general {Hamiltonian} mechanics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {344--355},
year = {1984},
volume = {60},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a1/}
}
TY - JOUR
AU - V. S. Buslaev
AU - E. A. Nalimova
TI - Trace formula in general Hamiltonian mechanics
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 1984
SP - 344
EP - 355
VL - 60
IS - 3
UR - http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a1/
LA - ru
ID - TMF_1984_60_3_a1
ER -
%0 Journal Article
%A V. S. Buslaev
%A E. A. Nalimova
%T Trace formula in general Hamiltonian mechanics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 344-355
%V 60
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a1/
%G ru
%F TMF_1984_60_3_a1
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.
