Structure of the energy tensor in the classical electrodynamics of point particles

Abstract

Classical electromagnetic theory provides an energy tensor defined off the particle's world line. The definition is extended to a distribution valid "everywhere." The extended definition is essentially unique. The Lorentz-Dirac equation follows immediately without the appearance of infinities at any stage. In the distribution theory formulation momentum integrals over spacelike planes exist and are finite. The planes are not restricted to be orthogonal to the particles' world lines, and consequently a finite, conserved momentum integral exists for a system of charged particles. "Self-momentum" (the "momentum" due to the strongest singularities in the energy tensor) is conserved differentially for each particle separately, and the associated integral over a spacelike plane is zero. It may therefore be omitted. This justifies and generalizes the ad hoc procedure of dropping self-energy terms in electrostatics.