Interference in the radiation of two point-like charges

TL;DR

This paper analyzes the electromagnetic energy-momentum and angular momentum of two moving point charges, decomposing fields into bound and radiative parts, and derives the Lorentz-Dirac equation considering mutual interactions.

Contribution

It provides a detailed decomposition of electromagnetic fields into bound and radiative components for two charges and derives their equations of motion including mutual interactions.

Findings

Bound terms deform electromagnetic clouds of charges

Radiative terms define escaping radiation

Lorentz-Dirac equation derived for interacting charges

Abstract

Energy-momentum and angular momentum carried by electromagnetic field of two point-like charged particles arbitrarily moving in flat spacetime are presented. Apart from usual contributions to the Noether quantities produced separately by particles 1 and 2, the conservation laws contain also joint contribution due to the fields of both particles. The mixed part of Maxwell energy-momentum density is decomposed into bound and radiative components which are separately conserved off the world lines of particles. The former describes the deformation of electromagnetic clouds of ``bare'' charges due to mutual interaction while the latter defines the radiation which escapes to infinity. The bound terms contribute to particles' individual 4-momenta while the radiative ones exert the radiation reaction. Analysis of energy-momentum and angular momentum balance equations results the Lorentz-Dirac equation as an equation of motion for a pointed charge under the influence of its own electromagnetic field as well as field produced by another charge.