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

P. V. Buividovich·V. I. Kuvshinov
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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.

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P. V. Buividovich, V. I. Kuvshinov. 2006-05-21. Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields. https://doi.org/10.1103/physrevd.73.094015

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