Hard thermal loops from transport processes

The infrared limit of thermal gauge field dynamics in Minkowski space can be represented by the local interaction of the classical gauge field with a thermal plasma of classical colored particles. A lattice formulation of this dynamical system can be derived which conserves all important symmetries and lends itself to numerical simulation. We have verified that the HTL dispersion relations known from perturbation theory are well reproduced, and we have confirmed the Arnold-Son-Yaffe scaling relation for the Chern-Simons number diffusion rate in the Yang-Mills-Higgs model. Two interesting generalizations for future work are: the study of the evolution of gauge field configurations far off equilibrium, such as they occur in relativistic heavy ion reactions, and the inclusion of hard interactions among the colored particles, generalizing the non-Abelian Vlasov equation to a non-Abelian Boltzmann equation and effectively introducing a color mean field into the parton cascade model. (author)