Finite Self-Energy of Classical Point Particles

The infinite mass self-energy difficulties of quantum field theory already occur, as is well-known, in the corresponding classical theories. Although cutoffs may be introduced to effect renormalization in both the classical and quantum cases, such procedures are physically unsatisfactory. We wish to point out in this note that at least for the static (Coulomb-type) contribution, one obtains finite results for the classical self-energies if the gravitational contribution to the total energy is included. Furthermore, it will be shown rigorously (in the static case) that the natural cutoff furnished by general relativity implies that all the mass of a point charge arises from its total self-field and that a neutral particle has no mass.