Some Properties of a Regularized Classical Electromagnetic Self-Interaction

Abstract

Classical electrodynamics is conventionally formulated in terms of fields and charge sources, and a coupling between the two. Usually, the dynamics of either the sources or the fields are assumed known, from which the dynamics of the other are computed. The causal loop may be iterated, for instance in the calculation of the non-linear optical susceptibilities. The loop may be closed by eliminating the fields from the dynamics resulting in an action wherein the sources appear to act upon themselves at a distance. In this formulation one sees that the action of a source upon itself is singular, and consequently the electromagnetic mass is infinite. For this reason, traditionally, the self-interaction terms are ignored and instead each of the sources is attributed with a finite Newtonian, non-electromagnetic, mass-action.

A more appealing approach is to render electromagnetic self-interaction finite, from which one would hope to derive the Newtonian mass-action whilst retaining — as closely as possible — the dynamical properties of the conventional formulation. In this paper we suggest a minimal modification to the classical electrodynamical action with these properties. The result is a modified and self-contained classical electrodynamics in which the sources have no intrinsic mass, but whose mass is acquired through electromagnetic self-interaction. The modification results in a description for the electron that may be regarded as a Lorentz-invariant extension of the Abraham-Lorentz model. An interesting feature of the new classical dynamics is its prediction of pair creation and annihilation events.