Radiation Reaction as a Non-conservative Force

TL;DR

This paper investigates radiation reaction as a non-conservative force using a Hamiltonian approach, showing its origin from the non-conservative part of the effective Lagrangian and relating it to a heat bath model.

Contribution

It applies Galley's Hamilton's principle for non-conservative systems to derive the radiation reaction force, aligning with classical results and providing a new perspective on its origin.

Findings

Radiation reaction arises from the non-conservative component of the effective Lagrangian.

The Hamiltonian formulation reproduces Jackson's equation of motion for a charged particle.

Modeling the radiation field as a heat bath justifies the non-conservative nature of radiation reaction.

Abstract

We study a system of a finite size charged particle interacting with radiation field by exploiting the Hamilton's principle for non-conservative system introduced recently by Galley[1]. The said formulation leads to the equation of motion of the charged particle that turns out to be the same as obtained by Jackson[3]. We show that radiation reaction stems from the non-conservative piece of the effective Lagrangian. We notice that a charge interacting with radiation field modeled as heat bath affords a way to justify that radiation reaction is a non-conservative force. The topic is suitable for graduate courses on advanced electrodynamics and classical theory of fields.