  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.
