A Boltzmann Equation for the QCD Plasma

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, where our equation coincides with that recently proposed 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.