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

2007/11/19 by S. N. Storchak, Storchak, S. N.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.0711.2910

34 pages

arxiv created 2007/11/19 · arxiv updated 2009/12/01

Abstract

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.

Related

• Path integrals on a manifold that is a product of the total space of the principal fiber bundle and the vector space
• Global Aspects of Quantizing Yang-Mills Theory
• Path integral on a manifold with a non-free group action
• Path integral representation of the quantum evolution in dynamical systems with a symmetry for the non-zero momentum level reduction
• A Stochastic Approach to the Definition of the Path Integral Measure