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As recent work continues to demonstrate, the study of relativistic scatteringprocesses leads to valuable insights and computational tools applicable to therelativistic bound-orbit two-body problem. This is particularly relevant in thepost-Minkowskian approach to the gravitational two-body problem, where thefield has only recently reached a full description of certain physicalobservables for scattering orbits, including radiative effects, at the thirdpost-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 particleand the total radiated linear momentum, in the relativistic classicalscattering of two point-charges, at sixth order in the charges (analogous to3PM order in gravity). We accomplish this here via direct iteration of theclassical equations of motion, while making comparisons where possible toresults from quantum scattering amplitudes, with the aim of contributing to theelucidation of conceptual issues and scalability on both sides. We also discussfurther extensions to radiative quantities of recently established relationswhich analytically continue certain observables from the scattering regime tothe regime of bound orbits, applicable for both the electromagnetic andgravitational cases.

Conservative and radiative dynamics in classical relativistic scattering and bound systems