Mean Field Dynamics in Non-Abelian Plasmas from Classical Transport Theory

TL;DR

This paper develops covariant equations from classical transport theory to describe mean field dynamics and fluctuations in non-Abelian plasmas, deriving B"odeker's effective theory near equilibrium.

Contribution

It introduces a general covariant framework for non-Abelian plasma dynamics and provides a method to derive collision integrals from microscopic theory.

Findings

Derived covariant equations for mean fields and fluctuations

Provided a procedure to obtain collision integrals from microscopic theory

Reproduced B"odeker's effective theory for soft fields near equilibrium

Abstract

Based on classical transport theory, we present a general set of covariant equations describing the dynamics of mean fields and their statistical fluctuations in a non-Abelian plasma in or out-of-equilibrium. A procedure to obtain the collision integrals for the Boltzmann equation from the microscopic theory is described. As an application, we study a hot non-Abelian plasma close to equilibrium, where the fluctuations are integrated out explicitly. For soft fields, and at logarithmic accuracy, we obtain B\"odeker's effective theory.