Trace formula in general Hamiltonian mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 344-355
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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.
@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},
publisher = {mathdoc},
volume = {60},
number = {3},
year = {1984},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a1/}
}
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/