On a gauge invariant description of soliton dynamics

TL;DR

This paper develops a gauge and diffeomorphism invariant framework for describing soliton dynamics, emphasizing that velocity-dependent modifications are dictated by symmetry principles, with an application to Yang-Mills theory on curved spacetime.

Contribution

It introduces a formalism for gauge invariant soliton dynamics that determines velocity-dependent terms solely from symmetry considerations.

Findings

Formalism ensures gauge and diffeomorphism invariance in soliton dynamics.

Explicit velocity-dependent modifications are derived from symmetry principles.

Application demonstrated for Yang-Mills theory on curved backgrounds.

Abstract

We present important elements of a gauge and diffeomorphism invariant formulation of the moduli space approximation to soliton dynamics. We argue that explicit velocity-dependent modifications are determined entirely from gauge and diffeomorphism invariance. We illustrate the formalism for the case of a Yang-Mills theory on a curved spacetime background.