Radiation reaction and renormalization for a photon-like charged particle

TL;DR

This paper develops a renormalization scheme for a massless charged particle, deriving an effective equation of motion based on energy-momentum and angular momentum balance, revealing unique behaviors compared to massive particles.

Contribution

It introduces a novel renormalization approach for massless charges and derives their effective equations of motion using electromagnetic tensor eigenvalues and eigenvectors.

Findings

Massless charges exhibit infinite radiation rates upon acceleration.

Effective equations of motion are based on electromagnetic tensor eigenvalues.

Uniform solutions correspond to motion along eigenvector directions.

Abstract

A renormalization scheme which relies on energy-momentum and angular momentum balance equations is applied to the derivation of effective equation of motion for a massless point-like charge. Unlike the massive case, the rates of radiated energy-momentum and angular momentum tend to infinity whenever the source is accelerated. The external electromagnetic fields which do not change the velocity of the particle admit only its presence within the interaction area. The effective equation of motion is the equation on eigenvalues and eigenvectors of the electromagnetic tensor. The massless charges move along base line determined by the eigenvectors when the effective equation of motion possesses uniform solutions. It is interesting that the same solution arises in Rylov's model of magnetosphere of a rapidly rotating neutron star (pulsar).