Dependent coordinates in path integral measure factorization

Details Dependent coordinates in path integral measure factorization Dependent coordinates in path integral measure factorization

2003-11-23

arxiv.org/abs/math-ph/0311038v1

Physics

Mathematical Physics

LaTeX2e, 28 pages

Scientific paper

10.1088/0305-4470/37/27/011

The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for description of the diffusion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple unimodular Lie group. The transformation of the path integral, which factorizes the path integral measure, is based on the application of the optimal nonlinear filtering equation from the stochastic theory. The integral relation between the kernels of the original and reduced semigroup are obtained.

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