Radiation Reaction by Massive Particles and Its Non-Analytic Behavior

TL;DR

This paper derives a relativistic equation of motion for charged particles emitting massive radiation, revealing non-analytic mass dependence that challenges local derivative expansion approaches.

Contribution

It introduces a massive analog of the ALD equation and demonstrates its non-analytic behavior with respect to the radiation mass, which is a novel insight.

Findings

Radiation reaction term exhibits non-analytic dependence on mass M.

Derivative expansions in mass or 1/M are invalid for the massive ALD equation.

Specific motions analyzed show the non-local nature of radiation reaction.

Abstract

We derive a massive analog of the ALD (Abraham, Lorentz and Dirac) equation, i.e., the equation of motion of a relativistic charged particle with a radiation reaction term induced by emissions of massive fields. We show that the radiation reaction term has a non-analytic behavior as a function of the mass M of the radiation field and both expansions with respect of M and 1/M are generally invalid. Hence the massive ALD equation cannot be written as a local equation with derivative expansions. We especially investigate the radiation reaction in three specific motions, uniform acceleration, a circular motion and a scattering process.