Un-renormalized Classical Electromagnetism

Abstract

This paper follows in the tradition of direct-action versions of electromagnetism having the aim of avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass so as to arrive at a finite observed value. Given that, in this respect the direct-action approached ultimately failed because its initial exclusion of self-action was found to be untenable in the relativistic domain, this paper continues the tradition considering instead a version of electromagnetism wherein mechanical action is excluded and self-action is retained. It is shown that the resulting theory is effectively interacting due to the presence of infinite forces. A vehicle for the investigation is a pair of classical point charges in a positronium-like arrangement for which the orbits are found to be self-sustaining and naturally quantized.