On the Electromagnetic Energies and Forces

TL;DR

This paper investigates the longstanding issue of infinite electromagnetic energy associated with point charges, analyzing energies and forces through the lens of Distribution Theory to offer new insights.

Contribution

It introduces a novel approach to electromagnetic energies and forces using Distribution Theory, addressing the problem of infinite energy in classical and quantum contexts.

Findings

Reveals new perspectives on electromagnetic energy-momentum tensor

Provides a framework to handle infinities in point charge models

Enhances understanding of electromagnetic forces in distributional terms

Abstract

The problem of the `infinite energy' of a point charge is well known in connection with the Lorentz--Abraham--Dirac equation and, more significantly, in quantum electrodynamics. Though it is not stated usually, this is strongly related to the old problem of what the electromagnetic energy-momentum tensor is. Electromagnetic energies and forces will be examined thoroughly from a new point of view in the framework of Distribution Theory.