Thermalization algorithms for classical gauge theories

TL;DR

This paper introduces a Langevin-based algorithm for thermalizing classical gauge theories that exactly preserves Gauss' constraints, demonstrated on SU(2) gauge theories, including calculations of Lyapunov exponents.

Contribution

It presents a novel Langevin equation approach for thermalizing classical gauge theories while maintaining gauge constraints exactly.

Findings

Algorithm effectively thermalizes SU(2) gauge theories.

Computed Lyapunov exponents for SU(2) Yang-Mills theory.

Demonstrated preservation of Gauss' constraints during thermalization.

Abstract

I propose a method, based on a set of Langevin equations, for bringing classical gauge theories to thermal equilibrium while respecting the set of Gauss' constraints exactly. The algorithm is described in detail for the SU(2) gauge theory with or without the Higgs doublet. As an example of application, canonical average of the maximal Lyapunov exponent is computed for the SU(2) Yang-Mills theory.