Radiation reaction in higher-order electrodynamics

TL;DR

This paper derives a rigorous, history-dependent equation of motion for charged particles in higher-order electrodynamics, incorporating self-force effects from electromagnetic fields using distributional and variational methods.

Contribution

It provides a novel derivation of the self-force and equations of motion for charged particles in higher-order electrodynamics from fundamental principles.

Findings

Derived a world-line integral expression for self-force.

Established the equation of motion from a variational principle.

Confirmed the self-force matches previous averaging proposals.

Abstract

This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Land\'e--Thomas, and Podolsky. We rigorously derive a world-line integral expression for the self-force of the charged particle from a distributional equation for the conservation of four-momentum only. This naturally leads to an equation of motion for charged particles that incorporates a history-dependent self-interaction. We show additionally that the same equation of motion follows from a variational principle for retarded fields. The self-force coincides with an expression proposed by Zayats and Gratus--Perlick--Tucker on the basis of an averaging procedure.