Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields

Details Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields

2006-05-21

arxiv.org/abs/hep-th/0605207v1

Phys.Rev. D73 (2006) 094015

Physics

High Energy Physics

High Energy Physics - Theory

7 pages

Scientific paper

10.1103/PhysRevD.73.094015

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.

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