Equations of a relative equilibrium in Yang-Mills theory

TL;DR

This paper derives equations describing relative equilibria in pure Yang-Mills gauge theory with Coulomb gauge fixing, linking gauge theory dynamics to finite-dimensional systems with symmetry.

Contribution

It introduces a new set of equations for relative equilibria in Yang-Mills theory, extending previous work on Wong's equations and connecting to dynamical systems with symmetry.

Findings

Derived equations for relative equilibria in Yang-Mills theory.

Established similarity to finite-dimensional dynamical systems with symmetry.

Linked gauge theory dynamics to reduced motion descriptions.

Abstract

The equations of a relative equilibrium in a pure Yang--Mills gauge theory with the Coulomb gauge fixing are obtained. They are derived as a direct consequence of the results of our previous work on Wong's equations in gauge theory.The obtained equations are similar to the equations of a relative equilibrium in reducible finite-dimensional dynamical systems with a symmetry. In all these equations, the description of the reduced motion is performed by making use of the dependent coordinates.