Hard Thermal Loops from Transport Processes

Because the running coupling g(T ) of QCD decreases as a function of temperature T , the SU(3) color gauge theory becomes weakly coupled in the high temperature limit. Numerical simulations of the lattice gauge theory with dynamical quarks have shown that the equation of state ǫ(T ) makes a transition from the low-temperature phase, where the effective degrees of freedom are hadrons, to a high temperature phase, where quarks and gluons can be excited independently. The transition temperature is Tc ≈ 150 MeV. Already in perturbation theory one finds that the quasiparticle excitations in the high-temperature phase are not massless. At low momenta, k < gT ≪ T (we are here considering the weak coupling limit), there are three propagating collective modes with frequency