Stability and mass of point particles

Abstract

In this paper we consider classical point particles in full interaction with an arbitrary number of dynamical scalar and (abelian) vector fields. It is shown that the requirement of stability ---vanishing self-force--- is sufficient to remove the well-known inconsistencies of the classical theory: the divergent self-energy, as well as the failure of Lorentz-covariance of the energy-momentum when including the contributions of the fields. As a result, in these models the mass of a point particle becomes finitely computable. It is shown how these models are connected to quantum field theory via the path-integral representation of the propagator.