Radiation reaction and renormalization via conservation laws of the Poincare group

TL;DR

This paper develops a Poincaré-invariant regularization method for classical electrodynamics in 4D and 6D, deriving radiation reaction forces and revealing internal angular momentum in 6D, establishing the theory's renormalizability.

Contribution

It introduces a symmetry-based regularization approach and demonstrates the renormalizability of 6D electrodynamics with internal angular momentum.

Findings

Derived radiation reaction forces in 4D and 6D.

Showed 6D point charge has internal angular momentum proportional to acceleration squared.

Established 6D electrodynamics as a renormalizable theory.

Abstract

We consider the self-action problem in classical electrodynamics of a point-like charge arbitrarily moving in flat 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 magnitude which is proportional to the square of acceleration. 6D action functional contains, apart from 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 {\it Poincar\'e-invariant} six-dimensional electrodynamics is renormalizable theory.