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Perturbative and non-perturbative aspects of the non-abelian Boltzmann-Langevin equation

Dietrich Bodeker
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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^2T 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.

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Dietrich Bodeker. 2002-09-11. Perturbative and non-perturbative aspects of the non-abelian Boltzmann-Langevin equation. https://doi.org/10.1016/s0550-3213(02)00841-6

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