The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of modern renormalization theory

TL;DR

This paper derives the classical electron equations of motion using renormalization techniques, showing how the Lorentz-Dirac equation simplifies to the Landau-Lifshitz form without requiring quantum theory knowledge.

Contribution

It introduces a renormalization-based derivation of classical electron equations, connecting the Lorentz-Dirac and Landau-Lifshitz equations in a straightforward, elementary manner.

Findings

Derivation of Lorentz-Dirac equation from Maxwell-Lorentz equations.

Reduction to Landau-Lifshitz equation for large-scale electron motions.

No need for quantum field theory concepts in the derivation.

Abstract

This paper uses elementary techniques drawn from renormalization theory to derive the Lorentz-Dirac equation for the relativistic classical electron from the Maxwell-Lorentz equations for a classical charged particle coupled to the electromagnetic field. I show that the resulting effective theory, valid for electron motions that change over distances large compared to the classical electron radius, reduces naturally to the Landau-Lifshitz equation. No familiarity with renormalization or quantum field theory is assumed.