Variational principle and energy-momentum tensor for relativistic Electrodynamics of point charges

TL;DR

This paper introduces a new Lorentz-invariant regularization method for the energy-momentum tensor in relativistic electrodynamics of point charges, avoiding divergences and deriving known equations from a covariant action.

Contribution

It presents a novel regularization and renormalization approach that yields a divergence-free, symmetric, and conserved energy-momentum tensor for charged point particles in a covariant framework.

Findings

A new tempered distribution representation of the energy-momentum tensor.

A covariant action leading to Lorentz-Dirac equations.

Extension of the method to charged p-branes and higher dimensions.

Abstract

We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical Electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions.