Stability and mass of point particles

TL;DR

This paper demonstrates that imposing stability conditions on classical point particles interacting with scalar and vector fields resolves longstanding issues like infinite self-energy and Lorentz covariance failure, making particle mass finite and connectable to quantum theory.

Contribution

It introduces a stability condition that ensures finite mass and resolves classical inconsistencies in point particle models with scalar and vector fields.

Findings

Stability condition removes divergent self-energy.

Lorentz covariance of energy-momentum is restored.

Particle mass becomes finitely computable.

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.