Path integral representation of the quantum evolution in dynamical systems with a symmetry for the non-zero momentum level reduction

Details Path integral representation of the quantum evolution in dynamical systems with a symmetry for the non-zero momentum level reduction Path integral representation of the quantum evolution in dynamical systems with a symmetry for the non-zero momentum level reduction

2009-12-17

arxiv.org/abs/0912.3509v1

Physics

Mathematical Physics

15 pages

Scientific paper

For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle Lie group, the path integral representation of the matrix Green's function, which describes the quantum evolution of the reduced motion, has been obtained. The integral relation between the path integrals representing the fundamental solutions of the parabolic differential equation defined on the total space of the principal fiber bundle and the linear parabolic system of the differential equations on the space of the sections of the associated covector bundle has been derived.

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