Geodesic
Trace formula in Hamiltonian mechanics
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 40-60

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The equation in variations, corresponding to a fixed interval of the trajectory of the Hamiltonian system of classical mechanics, generates a linear canonical differential operator. It is shown that for the ratio of such operators there exists a regularized determinant. The trace formula expresses this determinant in terms of the Jacobian of a certain transformation, given by the motion of the classical system and acting in a space having dimension equal to the number of degrees of freedom of the system. One notes the connection between the obtained relations and the quasiclassical asymptotics for the continual integral, describing the dynamics of the corresponding quantum system. 
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     author = {V. S. Buslaev and E. A. Rybakina},
     title = {Trace formula in {Hamiltonian} mechanics},
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     publisher = {mathdoc},
     volume = {115},
     year = {1982},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a3/}
}
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V. S. Buslaev; E. A. Rybakina. Trace formula in Hamiltonian mechanics. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 40-60. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a3/