Abstract. The transformation of the path integral measure under the reduction procedure in dynamical systems with a symmetry is considered. 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 semigroups is obtained.

PACS numbers: 03.65.Bz, 31.15.Kb

Print publication: Issue 27 (9 July 2004)
Received 22 July 2003, in final form 1 March 2004
Published 22 June 2004