An introduction to the Lorentz-Dirac equation

TL;DR

This paper introduces two derivations of the Lorentz-Dirac equation, highlighting its foundations and discussing interpretational challenges, aimed at readers with some background in differential geometry.

Contribution

It provides two distinct derivations of the Lorentz-Dirac equation, one based on radiation reaction and the other on energy-momentum conservation, clarifying its theoretical basis.

Findings

Two derivations of the Lorentz-Dirac equation presented

Discussion of interpretational difficulties included

Self-contained presentation with differential geometry prerequisites

Abstract

These notes provide two derivations of the Lorentz-Dirac equation. The first is patterned after Landau and Lifshitz and is based on the observation that the half-retarded minus half-advanced potential is entirely responsible for the radiation-reaction force. The second is patterned after Dirac, and is based upon considerations of energy-momentum conservation; it relies exclusively on the retarded potential. The notes conclude with a discussion of the difficulties associated with the interpretation of the Lorentz-Dirac equation as an equation of motion for a point charge. The presentation is essentially self-contained, but the reader is assumed to possess some elements of differential geometry (necessary for the second derivation only).