On Electrodynamical Self-Interaction

Abstract

It is shown that the classical Maxwell theory admits a simple and natural renormalization of the self-interaction energy. This leads to a consistent, local and causal, relativistic theory of the Maxwell field interacting with classical, charged, point–like particles. The theory may be regarded as a simple and necessary completion of special relativity. The renormalization method proposed here is a realization of Einstein’s idea of “deriving equations of motion from field equations”. It is shown that the Dirac’s “3-dots” equation does not describe a fundamental law of physics, but only a specific family of solutions of our theory, corresponding to a specific choice of the field initial data.