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

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.