Finite size corrections to the radiation reaction force in classical electrodynamics

TL;DR

It is proved that leading order effects due to the finite radius R of a spherically symmetric charge is order R2 rather than order R in any physical model, as widely claimed in the literature.

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 Poincaré 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.

Figures (2)

• Figure 1: The Feynman diagram giving the effective action, which when varied leads to the ALD radiation reaction equation, Eq. (\ref{['aldeq_1']}). The wiggly line represents a retarded photon and the double line indicates the charge's worldline, which is to be viewed as an external source coupling to the photon. The dot represents the coupling of the photon to the charge.
• Figure 2: Feynman diagrams needed for the first finite size corrections to the ALD equation. The $\otimes$ represents the coupling of the photon to the operator $O_2$.