Wong's equations in Yang-Mills theory

TL;DR

This paper derives Wong's equations for a particle on a Riemannian manifold with symmetry and extends these to pure Yang-Mills gauge theory, linking finite-dimensional dynamics with gauge field reduction.

Contribution

It provides a derivation of Wong's equations in the context of Yang-Mills theory using a geometric reduction approach.

Findings

Wong's equations are formulated in terms of dependent coordinates.

The equations are applied to pure Yang-Mills gauge theory with Coulomb gauge.

The approach links finite-dimensional dynamical systems with gauge field reduction.

Abstract

We derive Wong's equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semisimple Lie group. The obtained equations are written in terms of dependent coordinates which are typically used in an implicit description of the local dynamics given on the orbit space of the principal fiber bundle. Using these equations we obtain Wong's equations in a pure Yang--Mills gauge theory with the Coulomb gauge fixing. This result is based on the existing analogy between the reduction procedures carried out in our finite-dimensional dynamical system and in Yang-Mills gauge fields.