On the removal of divergences in electrodynamics: a global point of view

Abstract

This paper explores the implications of Dirac's seminal work on the concept of self-energy of a charged particle in classical electrodynamics. To avoid the notion of divergent acceleration through self-action, Dirac offered an alternative that involved the existence of preacceleration and an apparent departure from the inherent causality of special relativity. It is argued that Dirac's solution appears naturally in the electrodynamics described by action at a distance. In this framework the notion of self-action is replaced by that of the response of the universe on the large scale. Provided the universe has the correct large-scale structure, there are no divergent integrals either in the classical or the quantum version of electrodynamics. The price one has to pay involves replacing the purely local Lorentz invariant picture by a global cosmological one. On the other hand the price of standard renormalizable quantum electrodynamics is that of the theoretical mass of the electron is infinitely negative, a requirement that Dirac regarded as absurd, far worse than the loss of local invariance in favour of global invariance, the position adopted here.