Point Charges in Classical Electrodynamics

TL;DR

This paper reviews classical electrodynamics of point charges, focusing on the Lorentz-Dirac equation, self-interaction, and mass renormalization, with detailed mathematical derivations and computational tools.

Contribution

It provides a comprehensive review of the Lorentz-Dirac equation, including novel approaches to self-field definitions and detailed computational methods.

Findings

Derivation of Lorentz-Dirac equation via momentum balance

Analysis of self-interaction and mass renormalization

Mathematica tools for near-world-line field expansions

Abstract

LaTeX transcription (2025) of a 1989 honours thesis (University of Adelaide) on point charges in classical electrodynamics and the Lorentz-Dirac radiation-reaction equation. The thesis reviews the retarded field of an arbitrarily moving charge, energy-momentum conservation, and derives the Lorentz-Dirac equation via momentum balance. It discusses self-interaction and mass renormalization, and presents world-line self-field definitions including retarded averaging and an analytic continuation approach. Appendices include Mathematica listings used to obtain near-world-line expansions of the field and related quantities.