Perturbative and non-perturbative aspects non-Abelian Boltzmann–Langevin equation

Abstract

We study the Boltzmann–Langevin equation which describes the dynamics of hot Yang–Mills fields with typical momenta of order of the magnetic screening scale g 2 T. It is transformed into a path integral and Feynman rules are obtained. We find that the leading log Langevin equation can be systematically improved in a well behaved expansion in log(1/ g) −1. The result by Arnold and Yaffe that the leading log Langevin equation is still valid at next-to-leading-log order is confirmed. We also confirm their result for the next-to-leading-log damping coefficient, or color conductivity, which is shown to be gauge fixing independent for a certain class of gauges. The frequency scale g 2 T does not contribute to this result, but it does contribute, by power counting, to the transverse gauge field propagator. Going beyond a perturbative expansion we find 1-loop ultraviolet divergences which cannot be removed by renormalizing the parameters in the Boltzmann–Langevin equation.