Particle Motion in a Yang-Mills Field: Wong's Equations and Spin One-half Analogues

TL;DR

This paper develops a comprehensive Lagrangian framework for describing the classical motion of particles with internal symmetry in Yang-Mills fields, extending Wong's equations to include spin-$rac{1}{2}$ particles.

Contribution

It introduces a new, simple Lagrangian formalism for Wong's equations and generalizes them to spin-$rac{1}{2}$ particles in a gauge covariant manner.

Findings

Provides a natural Lagrangian description for particles in Yang-Mills fields.

Extends Wong's equations to include spin-$rac{1}{2}$ particles.

Offers a complete formalism for classical particle dynamics with internal degrees of freedom.

Abstract

A complete, straightforward and natural Lagrangian description is given for the classical non-relativistic dynamics of a particle with colour or internal symmetry degrees of freedom moving in a background Yang-Mills field. This provides a new simple Lagrangian formalism for Wong's equations for spinless particles, and presents also their generalisation, in gauge covariant form, for spin-$\frack$ particles, within a complete Lagrangian formalism.