The alternative to classical mass renormalization for tube-based self-force calculations

TL;DR

This paper introduces a novel tube-based method for calculating electromagnetic self-force that eliminates the need for classical mass renormalization, enabling exact calculations for finite-sized radiating systems.

Contribution

It presents a new tube method that avoids mass renormalization, providing a more rigorous approach to self-force calculations in classical electromagnetism.

Findings

Exact self-force calculations for finite-sized systems are now possible.

A new derivation of the Lorentz-Dirac equation is provided.

Potential application to gravitational self-force problems is discussed.

Abstract

To date, classical mass renormalization has been invoked in all tube-based self-force calculations, thus following the method introduced in Dirac's 1938 calculation of the electromagnetic self-force for the classical radiating electron. In this paper a new tube method is described that does not rely on a mass renormalization procedure. As a result, exact self-force calculations become possible for classical radiating systems of finite size. A new derivation of the Lorentz-Dirac equation is given and the relationship between the new tube method and the classical mass renormalization procedure is explained. It is expected that a similar tube method could be used to obtain rigorous results in the gravitational self-force problem.