Point Charges in Classical Electrodynamics

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.

💡 Research Summary

This document is a modern LaTeX transcription of Jonathan N. E. Baxter’s 1989 honours thesis from the University of Adelaide, titled “Point Charges in Classical Electrodynamics”. The thesis provides a comprehensive treatment of the classical theory of point charges, focusing on the derivation and interpretation of the Lorentz–Dirac radiation‑reaction equation, the role of self‑interaction, and the problem of mass renormalisation.

Chapter 2 introduces Maxwell’s equations in tensor form, adopts the Lorenz gauge, and solves the wave equation for the four‑potential of a point charge using Green’s functions. The resulting Liénard–Wiechert potentials are expressed in terms of the retarded proper time τ₍ᵣ₎, the scalar distance ρ = −r·v, and the four‑velocity v^μ. A detailed calculus of variations is developed for functions that depend on τ₍ᵣ₎, yielding identities such as ∂_μτ₍ᵣ₎ = −r_μ/ρ and the explicit form of the field tensor
F^{μν}=e