# Self-interaction in classical gauge theories and gravitation

## TL;DR

This paper explores the manifestations of self-interaction in classical gauge theories and gravitation, focusing on topological phases, degrees of freedom, and the physical implications of these phenomena.

## Contribution

It provides a systematic analysis of self-interaction manifestations, including topological phases and degrees of freedom rearrangements, in gauge theories and general relativity.

## Key findings

- Rearranged Maxwell-Lorentz electrodynamics describes dressed particles and radiation.
- Topological phases occur in pure field systems.
- Ambiguities in energy and momentum in systems with topological content like black holes.

## Abstract

To develop a systematic treatment of the self-interaction problem in classical gauge theories and general relativity, we study tenable manifestations of self-interaction: topological phases, and rearrangements of degrees of freedom appearing in the action. We outline the occurrence of topological phases in pure field systems. We show that the rearranged Maxwell-Lorentz electrodynamics is a mathematically consistent and physically satisfactory theory which describes new entities, dressed charged particles and radiation. We extend this analysis to cover different modifications of the Maxwell-Lorentz electrodynamics and the SU(N) Yang-Mills-Wong theory. We take a brief look at a subtle mechanism of self-interaction in classical strings. Turning to general relativity, we note that the total energy and momentum of a system with nontrivial topological content, such as a black hole, are ambiguous, coordinatization-dependent quantities, which resembles the situation with paradoxical decompositions in the Banach-Tarski theorem.