Self force in 2+1 electrodynamics

TL;DR

This paper investigates the radiation reaction for a point charge in 2+1 dimensional electrodynamics, proposing a regularization method to handle divergences and deriving an effective equation of motion including self-force effects.

Contribution

It introduces a Poincaré-invariant regularization procedure and derives a finite, effective equation of motion for a radiating charge in 2+1 dimensions.

Findings

Regularization removes divergences from point charge self-action.

Effective equations incorporate non-local self-force terms.

The approach ensures conservation of energy-momentum and angular momentum.

Abstract

The radiation reaction problem for an electric charge moving in flat space-time of three dimensions is discussed. The divergences stemming from the pointness of the particle are studied. A consistent regularization procedure is proposed, which exploits the Poincar\'e invariance of the theory. Effective equation of motion of radiating charge in an external electromagnetic field is obtained via the consideration of energy-momentum and angular momentum conservation. This equation includes the effect of the particle's own field. The radiation reaction is determined by the Lorentz force of point-like charge acting upon itself plus a non-local term which provides finiteness of the self-action.