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

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.