Electrodynamics Classical Inconsistencies

TL;DR

This paper resolves classical electrodynamics inconsistencies related to the electron’s self-field by emphasizing the importance of null off the charge world line terms, showing no need for renormalization or modifications to Maxwell's theory.

Contribution

It demonstrates that classical electrodynamics issues stem from neglecting certain null off the world line terms, establishing the self-field stress tensor as integrable without causality or energy conservation conflicts.

Findings

Self-field stress tensor of a point electron is integrable.

No causality violation occurs in the corrected framework.

Renormalization or modifications to Maxwell's theory are unnecessary.

Abstract

The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world line but that gives a non null contribution on its world line. The self-field stress tensor of a point classical electron is integrable, there is no causality violation and no conflict with energy conservation in its equation of motion, and there is no need of any kind of renormalization nor of any change in the Maxwell's theory for this. (This is part of the paper hep-th/9510160, stripped , for simplicity, of its non-Minkowskian geometrization of causality and of its discussion about the physical meaning of the Maxwell-Faraday concept of field).