Regularizations of point charges, the Li\'{e}nard-Wiechert potential, and the electron self-energy

TL;DR

This paper uses Colombeau regularization to analyze the electromagnetic field of a point charge, deriving the Lie9nard-Wiechert potential and discussing electron self-energy within Minkowski space.

Contribution

It introduces a Colombeau-type regularization approach to derive electromagnetic potentials and analyze electron self-energy in a rigorous mathematical framework.

Findings

Derived the Lie9nard-Wiechert potential using generalized functions.

Analyzed the electron self-energy and singularity in the rest frame.

Provided a geometric interpretation of electromagnetic fields of point charges.

Abstract

We apply Colombeau-type regularization to the electromagnetic field of a point-charge and show how the Li\'{e}nard-Wiechert potential can be derived from a generalized function based on the geometry of Minkowski space. Furthermore, for a charged particle in its rest frame, we discuss the electric monopole, magnetic dipole, electron singularity, and self-energy.