A Boltzmann Equation for the QCD Plasma

TL;DR

This paper derives a Boltzmann equation for the QCD plasma from quantum field equations, connecting it to existing effective theories and analyzing collision term cancellations affecting transport coefficients.

Contribution

It provides a gauge covariant derivation of the Boltzmann equation for the QCD plasma, linking it to B"odeker's effective theory and analyzing collision term cancellations.

Findings

Recovery of B"odeker's effective theory for long wavelength fluctuations

Identification of cancellations in collision terms affecting transport coefficients

Discussion of limitations of the gradient expansion when interaction ranges are large

Abstract

We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge covariant gradient expansion which takes consistently into account all possible dependences on the gauge coupling assumed to be small. We point out a limitation of the gradient expansion arising when the range of the interactions becomes comparable with that of the space-time inhomogeneities of the system. The method is first applied to the case of scalar electrodynamics, and then to the description of long wavelength colour fluctuations in the QCD plasma. In the latter case, we recover B\"odeker's effective theory and its recent reformulation by Arnold, Son and Yaffe. We discuss interesting cancellations among various collision terms, which occur in the calculation of most transport coefficients, but not in that of the quasiparticle lifetime, or in that of the relaxation time of colour excitations.