S N Storchak 2004 J. Phys. A: Math. Gen. 37 7019 doi:10.1088/0305-4470/37/27/011
S N Storchak
Show affiliationsThe 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.
05.45.-a Nonlinear dynamics and nonlinear dynamical systems
02.30.Hq Ordinary differential equations
02.20.Qs General properties, structure, and representation of Lie groups
58D17 Manifolds of metrics (esp. Riemannian)
22E46 Semisimple Lie groups and their representations
81Rxx Groups and algebras in quantum theory
81Sxx General quantum mechanics and problems of quantization
Issue 27 (9 July 2004)
Received 22 July 2003, in final form 1 March 2004
Published 22 June 2004
S N Storchak 2004 J. Phys. A: Math. Gen. 37 7019
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