Classical mechanics of relativistic particle with colour

TL;DR

This paper develops a classical framework for relativistic particles with intrinsic color degrees of freedom, integrating gauge interactions and internal dynamics through a geometric Lagrangian approach.

Contribution

It introduces a novel classical model for relativistic particles with color, combining external gauge interactions and internal degrees of freedom within a geometric Lagrangian and Hamiltonian framework.

Findings

External dynamics follow Wong equations for gauge interactions.

Internal dynamics lead to spatial motion determined by integrals of motion.

A Hamiltonian formulation consistent with the Lagrangian approach is constructed.

Abstract

Classical description of relativistic pointlike particle with intrinsic degrees of freedom such as isospin or colour is proposed. It is based on the Lagrangian of general form defined on the tangent bundle over a principal fibre bundle. It is shown that the dynamics splits into the external dynamics which describes the interaction of particle with gauge field in terms of Wong equations, and the internal dynamics which results in a spatial motion of particle via integrals of motion only. A relevant Hamiltonian description is built too.