Classical transport theory and hard thermal loops in the quark-gluon plasma

Abstract

Classical transport theory for colored particles is investigated and employed to derive the hard thermal loops of QCD. A formal construction of phase space for color degrees of freedom is presented. The gauge invariance of the non-Abelian Vlasov equations is verified and used as a guiding principle in our approximation scheme. We then derive the generating functional of hard thermal loops from a constraint satisfied at leading order by the color current. This derivation is more direct than alternative ones based on perturbative quantum field theory, and shows that hard thermal effects in hot QCD are essentially classical. As an illustration, we analyze color polarization in the QCD plasma.