Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields
arXiv:hep-th/0605207 · doi:10.1103/PhysRevD.73.094015
Abstract
A general equation for the probability distribution of parallel transporters on the gauge group manifold is derived using the cumulant expansion theorem. This equation is shown to have a general form known as the Kramers-Moyall cumulant expansion in the theory of random walks, the coefficients of the expansion being directly related to nonperturbative cumulants of the shifted curvature tensor. In the limit of a gaussian-dominated QCD vacuum the obtained equation reduces to the well-known heat kernel equation on the group manifold.
arXiv comment7 pages
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