Radiation Reaction, Renormalization and Poincar\'e Symmetry

TL;DR

This paper investigates the self-action problem in classical electrodynamics for massive and massless charges, proposing a symmetry-based regularization, deriving radiation reaction forces, and analyzing energy-momentum radiation and interactions.

Contribution

It introduces a symmetry-based regularization method, derives radiation reaction forces in 4D and 6D, and demonstrates the renormalizability of 6D electrodynamics for massive charges.

Findings

Radiation reaction forces are derived in 4D and 6D.

6D electrodynamics of massive charges is renormalizable.

Energy-momentum radiation rates tend to infinity for accelerated massless charges.

Abstract

We consider the self-action problem in classical electrodynamics of a massive point-like charge, as well as of a massless one. A consistent regularization procedure is proposed, which exploits the symmetry properties of the theory. The radiation reaction forces in both 4D and 6D are derived. It is demonstrated that the Poincar\'e-invariant six-dimensional electrodynamics of the massive charge is renormalizable theory. Unlike the massive case, the rates of radiated energy-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 for eigenvalues and eigenvectors of the electromagnetic tensor. The interference part of energy-momentum radiated by two massive point charges arbitrarily moving in flat spacetime is evaluated. It is shown that the sum of work done by Lorentz forces of charges acting on one another exhausts the effect of combination of outgoing electromagnetic waves generated by the charges.