Perturbative and non-perturbative aspects non-Abelian Boltzmann–Langevin equation Original Research Article

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 g2T. 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 g2T 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.