Variational principle and energy–momentum tensor for relativistic electrodynamics of point charges

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.