Dependent coordinates in path integral measure factorization

Abstract

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.

LaTeX2e, 28 pages

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Cited by in corpus (5)

• On the geometrical representation of the path integral reduction Jacobian: The case of dependent coordinates in the description of the reduced motion
• Wong's equations in Yang-Mills theory
• On geometrical representation of the Jacobian in a path integral reduction problem
• The Lagrange-Poincaré equations for interacting Yang-Mills and scalar fields
• Path integral representation of the quantum evolution in dynamical systems with a symmetry for the non-zero momentum level reduction