Electrodynamics of massless charged particles

TL;DR

This paper rigorously derives the classical dynamics of massless charged particles from fundamental principles, showing they do not radiate or self-interact, and establishing a consistent framework for their interactions.

Contribution

It provides a first-principles derivation of massless charged particle dynamics, handling singularities and proving the existence of a conserved energy-momentum tensor without an action principle.

Findings

Massless charged particles obey Lorentz equations without radiation reaction.

The energy-momentum tensor for these particles is well-defined and conserved.

Massless charged particles do not emit bremsstrahlung or self-interact.

Abstract

We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b) Lorentz- and reparameterization-invariance, c) local conservation of energy and momentum. Despite the presence of pronounced singularities of the electromagnetic field along Dirac-like strings, we give a constructive proof of the existence of a unique distribution-valued energy-momentum tensor. Its conservation requires the particles to obey standard Lorentz equations and they experience, hence, no radiation reaction. Correspondingly the dynamics of interacting classical massless charged particles can be consistently defined, although they do not emit bremsstrahlung end experience no self-interaction.