The theory of the electromagnetic self-force according to conformal symmetry

Abstract

Writing a conformal invariant electrodynamics over space-time sphere space, suggested originally by the conformal invariance of the Maxwell theory, leads unambiguously to a mathematically nonsingular theory of the classical self-force. The new degree of freedom λ, geometrically the sphere radius, has the physical meaning of a minimum nonzero time lag in causal signal propagation. The nonsingular self-force, the absence of Coulomb infinities, the finite e.m. mass renormalization are directly due to the presence of λ. Conformal invariance essentially alone fixes the model of a finite particle, which is both «point» and «extended» at the same time, however «extended in time» rather than spatially. Only retarded fields are used, and no approximations are made. In the lowest orders of a perturbation theory in powers of the classical radius, one recovers the Lorentz equation and (with an important difference) the Lorentz-Dirac equation.