Universal Self Force from an Extended-Object Approach

TL;DR

This paper develops a consistent extended-object method to determine the self force on an accelerating charged particle, resolving divergence issues and deriving a universal expression aligned with Dirac's formula.

Contribution

It introduces a fix to previous divergence problems in the extended-object approach, providing a universal self force expression that matches established results.

Findings

Resolved divergence issues in the extended-object self force calculation

Derived a universal self force expression consistent with Dirac's formula

Provided a clearer understanding of the origin of divergence problems

Abstract

We present a consistent extended-object approach for determining the self force acting on an accelerating charged particle. In this approach one considers an extended charged object of finite size $\epsilon $, and calculates the overall contribution of the mutual electromagnetic forces. Previous implementations of this approach yielded divergent terms $\propto 1/\epsilon $ that could not be cured by mass-renormalization. Here we explain the origin of this problem and fix it. We obtain a consistent, universal, expression for the extended-object self force, which conforms with Dirac's well known formula.