Geodesic
Trace formula in general Hamiltonian mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 344-355 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     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
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/

[1] Kac M., Integration in Function Spaces and Some of Its Applications, Pisa, 1980, 82 pp. | MR

[2] Buslaev V. S., DAN SSSR, 182:4 (1968), 743–746 | MR | Zbl

[3] Vasilev A. N., Funktsionalnye metody v kvantovoi teorii polya i statistike, LGU, L., 1976, 295 pp.

[4] Buslaev V. S., Rybakina E. A., “Formula sleda v gamiltonovoi mekhanike”, Zap. nauchn. semin. LOMI, 115, 1982, 40–60 | MR | Zbl

[5] Bayen F., Flato M., Fronsdal C., Lichnerowicz A., Sternheimer D., Ann. of Phys., 111:1 (1978), 61–110 | DOI | MR | Zbl

[6] Gokhberg I. Ts., Krein M. G., Teoriya volterrovykh operatorov v gilbertovom prostranstve, Nauka, M., 1967, 508 pp. | MR