Conservative and radiative dynamics in classical relativistic scattering and bound systems

TL;DR

This paper computes the relativistic momentum changes and radiated energy in classical electromagnetic scattering of point charges at sixth order, providing insights relevant to gravitational two-body problems and comparing classical and quantum approaches.

Contribution

It presents the first calculation of momentum changes and radiation in relativistic charge scattering at sixth order, extending classical results and connecting to quantum scattering amplitudes.

Findings

Computed momentum changes for two charges in relativistic scattering.

Quantified total radiated momentum at sixth order in charges.

Compared classical results with quantum scattering amplitude predictions.

Abstract

As recent work continues to demonstrate, the study of relativistic scattering processes leads to valuable insights and computational tools applicable to the relativistic bound-orbit two-body problem. This is particularly relevant in the post-Minkowskian approach to the gravitational two-body problem, where the field has only recently reached a full description of certain physical observables for scattering orbits, including radiative effects, at the third post-Minkowskian (3PM) order. As an historically instructive simpler example, we consider here the analogous problem in electromagnetism in flat spacetime. We compute for the first time the changes in linear momentum of each particle and the total radiated linear momentum, in the relativistic classical scattering of two point-charges, at sixth order in the charges (analogous to 3PM order in gravity). We accomplish this here via direct iteration of the classical equations of motion, while making comparisons where possible to results from quantum scattering amplitudes, with the aim of contributing to the elucidation of conceptual issues and scalability on both sides. We also discuss further extensions to radiative quantities of recently established relations which analytically continue certain observables from the scattering regime to the regime of bound orbits, applicable for both the electromagnetic and gravitational cases.