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arXiv · 2604.01004

Modeling of point charges with distributions, regularizations, and generalized functions

Guenther Hoermann·Nathalie Tassotti
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Abstract

We apply regularization and generalized function techniques to the classical electromagnetic field of a point-charge, following a strategy by the physicist A. Gsponer 2007-2009, thereby extending it and adding rigor.. We show how the Li\'{e}nard-Wiechert potential emerges essentially from the basic geometry of Minkowski space, namely by action of the d'Alembertian on a generating vector field, which is defined via a spacetime interval between an observer and the point-charge at retarded proper time. Furthermore, for a charged particle in its rest frame, we discuss generalized functions aspects of the electric monopole, magnetic dipole, electron singularity, and self-energy, where infinitely large generalized numbers occur whose concrete representations can be applied in field renormalization.

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Guenther Hoermann, Nathalie Tassotti. 2026-04-01. Modeling of point charges with distributions, regularizations, and generalized functions. https://arxiv.org/abs/2604.01004

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