A Comment on the Classical Electron Self-Energy

TL;DR

This paper analyzes the divergence issue of electron self-energy in classical electrodynamics, proposing a distribution-based extension that renders the self-energy an undetermined constant, which can be fixed empirically.

Contribution

It introduces a novel distributional approach to handle electron self-energy divergence, showing it as an undetermined constant that can be fixed through empirical data.

Findings

Self-energy divergence can be treated as an undetermined constant.

Distribution theory provides a framework for renormalization.

Empirical fixing of the self-energy value is possible.

Abstract

This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight, electrostatics implies a divergence once we treat the electron as a charged point particle. However, our construction shows that its self-energy turns out to be an undetermined constant upon renormalization. Appealing to empirical results we may fix its value, demanding, for example, that all its mass comes from an electrostatic origin.