The exact radiation-reaction equation for a classical charged particle

TL;DR

This paper proposes a novel, exact relativistic equation of motion for a classical charged particle that is non-perturbative and variational, addressing a longstanding problem in classical electrodynamics.

Contribution

It introduces a variational derivation of the exact radiation-reaction equation using a hybrid Hamilton principle and self-field treatment.

Findings

Derivation of a non-perturbative, exact RR equation

The RR equation is shown to be necessarily variational

Provides a new theoretical framework for classical charged particle dynamics

Abstract

An unsolved problem of classical mechanics and classical electrodynamics is the search of the exact relativistic equations of motion for a classical charged point-particle subject to the force produced by the action of its EM self-field. The problem is related to the conjecture that for a classical charged point-particle there should exist a relativistic equation of motion (RR equation) which results both non-perturbative, in the sense that it does not rely on a perturbative expansion on the electromagnetic field generated by the charged particle and non-asymptotic, i.e., it does not depend on any infinitesimal parameter. In this paper we intend to propose a novel solution to this well known problem, and in particular to point out that the RR equation is necessarily variational. The approach is based on two key elements: 1) the adoption of the relativistic hybrid synchronous Hamilton variational principle recently pointed out (Tessarotto et al, 2006). Its basic feature is that it can be expressed in principle in terms of arbitrary "hybrid" variables (i.e., generally non-Lagrangian and non-Hamiltonian variables); 2) the variational treatment of the EM self-field, taking into account the exact particle dynamics.