Finite size corrections to the radiation reaction force in classical electrodynamics

TL;DR

This paper develops an effective field theory to analyze how finite size affects electromagnetic radiation reaction forces, revealing that leading corrections scale with the square of the size, not linearly, due to symmetry constraints.

Contribution

It demonstrates that finite size corrections to radiation reaction are of order R^2, not R, due to Poincaré and gauge symmetries, and calculates the leading correction to the Abraham-Lorentz-Dirac force.

Findings

Leading order finite size effects are proportional to R^2.

Linear corrections in R are excluded by symmetries.

Explicit calculation of the correction to the Abraham-Lorentz-Dirac force.

Abstract

We introduce an effective field theory approach that describes the motion of finite size objects under the influence of electromagnetic fields. We prove that leading order effects due to the finite radius $R$ of a spherically symmetric charge is order $R^2$ rather than order $R$ in any physical model, as widely claimed in the literature. This scaling arises as a consequence of Poincar\'e and gauge symmetries, which can be shown to exclude linear corrections. We use the formalism to calculate the leading order finite size correction to the Abraham-Lorentz-Dirac force.