Can classical electrodynamics be renormalized?

A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles is proposed. The Lorentz force, which is ill defined due to Maxwell equations, is replaced by a suitable boundary condition for the behaviour of the field in the neighbourhood of the particle. The theory is derived from a classical “soliton-like” model of an extended particle. An approximation procedure for such a model is developed, which leads to a mathematically consistent theory, where the particle is described completely by its position and velocity. The resulting theory is universal (i.e. does not depend upon a specific model we start with) and may be regarded as a simple and necessary completion of special relativity. The theory is “already renormalized” i.e. no infinities arise.