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 {\it classical}. As an illustration, we analyze color polarization in the QCD plasma.