An effective theory for omega << k << gT color dynamics in hot non-Abelian plasmas

TL;DR

This paper develops an effective theoretical framework for analyzing long-wavelength color fluctuations in hot non-Abelian plasmas, bridging different scales and reformulating existing descriptions into a path integral form.

Contribution

It introduces a compact effective theory for omega << k << gT dynamics, extending Bodeker's description and providing a path integral formulation for these long-wavelength gauge fluctuations.

Findings

Provides a unified effective theory for omega << k << gT regime

Reformulates Bodeker's equations into a path integral

Enhances understanding of color dynamics at large scales

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 omega << k. I then give a compact way to package, in the omega << k limit, Bodeker's description of k << 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.