Radiation reaction and renormalization in classical electrodynamics of point particle in any dimension

TL;DR

This paper investigates radiation reaction and renormalization in classical electrodynamics for point particles across various dimensions, proposing a unified renormalization approach and deriving covariant equations in specific cases.

Contribution

It introduces a universal renormalization procedure applicable to all even dimensions and derives covariant equations of motion in three and six dimensions.

Findings

Classical electrodynamics is renormalizable in all dimensions except beyond four.

Explicit covariant equations are derived for three and six dimensions.

A unified renormalization framework is proposed for all even-dimensional cases.

Abstract

The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.