Radiation reaction and renormalization via conservation laws of the Poincaré group

Abstract

We consider the self-action problem in classical electrodynamics of a point-like charge arbitrarily moving in at space-time of four or six dimensions. A consistent regularization procedure is proposed which exploits the symmetry properties of the theory. The energy-momentum and angular momentum balance equations allow us to derive the radiation reaction forces in both 4D and 6D. It is shown that a point-like source in 6D possesses an internal angular momentum with the magnitude which is proportional to the square of acceleration. 6D action functional contains, apart from the usual bare mass, an additional renormalization constant which corresponds to the curvature of the world line (i. e. to the magnitude of internal angular momentum of bare particle). It is demonstrated that the Poincar e-invariant six-dimensional electrodynamics is renormalizable theory.