arXiv subjects

S. N. Storchak

Publications and source records attributed to S. N. Storchak.

20 records · Page 2Linked to original sources

arXiv2007

Path integral measure factorization in path integrals for diffusion of Yang--Mills fields

Factorization of the (formal) path integral measure in a Wiener path integrals for Yang--Mills diffusion is studied. Using the nonlinear filtering stochastic differential equation, we perform the transformation of the path integral defined on a total space of the Yang--Mills principal fiber bundle and come to the reduced path integral on a Coulomb gauge surface. Integral relation between the path integral representing the "quantum" evolution given on the original manifold of Yang--Mills fields and the path integral on the reduced manifold defined by the Coulomb gauge is obtained.

hep-th↗

arXiv2003

Dependent coordinates in path integral measure factorization

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.

math-ph↗