Covariant hamiltonian dynamics

TL;DR

This paper develops a covariant Hamiltonian framework for particles with gauge charges, introducing a method to find constants of motion using generalized Killing vectors and tensors, applied to monopole fields.

Contribution

It presents a novel covariant formalism and an algorithm for constructing constants of motion for particles in gauge fields, extending differential geometric tools.

Findings

Successfully applied to classical charges in monopole fields

Provides a systematic way to identify conserved quantities in gauge theories

Extends geometric methods to non-abelian gauge interactions

Abstract

We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of a generalization of the concept of Killing vectors and tensors in differential geometry. We apply the formalism to the motion of classical charges in abelian and non-abelian monopole fields