Finite self-interaction of the classical electromagnetic field

A nonlocal form of classical electrodynamics is considered by assuming a nonsingular modification of the Coulomb law at short distances. In the present approach, the electromagnetic self-mass of the particle is finite, the self-stress is zero, and the field at a sufficient distance from the source is described by retarded Lienard–Wiechert potentials, and the equation of motion of a particle with allowance for the self-interaction does not have runaway solutions and for a sufficiently smoothly varying external force is approximated to high accuracy by the Lorentz–Dirac equation (1).