Post-Coulombian Dynamics at Order 1.5

TL;DR

This paper analyzes the higher-order corrections to the dynamics of charged particles interacting with the electromagnetic field, focusing on dissipative effects due to radiation damping at order (v/c)^3.

Contribution

It provides an explicit derivation of radiation damping corrections at order (v/c)^3, extending previous work on Coulomb and Darwin corrections.

Findings

Dissipative corrections are derived at order (v/c)^3.

Radiation damping effects vanish if all particles share the same charge-to-mass ratio.

The analysis offers explicit control over error terms in the approximation.

Abstract

We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c, then in lowest order their motion is governed by the static Coulomb Lagrangian. We investigate higher order corrections with an explicit control on the error terms. The Darwin correction, order (v/c)^2, has been proved previously. In this contribution we obtain the dissipative corrections due to radiation damping, which are of order (v/c)^3 relative to the Coulomb dynamics. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.