Effective theory forω≪k≪gTcolor dynamics in hot non-Abelian plasmas

Abstract

A proper sequence of effective theories, corresponding to larger and larger distance scales, is crucial for analyzing real-time equilibrium physics in hot non-Abelian plasmas. For the study of color dynamics (by which I mean physics involving long wavelength gauge fluctuations), an important stepping stone in the sequence of effective theories is to have a good effective theory for dynamics with wave number k well below the Debye screening mass. I review how such dynamics is associated with inverse time scales $\ensuremath{\omega}\ensuremath{\ll}k.$ I then give a compact way to package, in the $\ensuremath{\omega}\ensuremath{\ll}k$ limit, B\"odeker's description of $k\ensuremath{\ll}m$ physics, which was in terms of Vlasov equations with collision terms. Finally, I show how the resulting effective theory can be reformulated as a path integral.