All Order Classical Electromagnetic Soft Theorems

TL;DR

This paper extends classical electromagnetic soft theorems by deriving an infinite set of subleading terms in the wave-form's late and early time expansions, applicable to scattering processes with only electromagnetic interactions.

Contribution

It introduces an infinite hierarchy of subleading terms in electromagnetic wave-forms, generalizing existing soft photon theorems for scattering events.

Findings

Derived an infinite set of subleading terms in wave-form expansions.

Obtained a resummed low-frequency electromagnetic wave-form.

Provided wave-form expressions at early and late times for two-particle scattering.

Abstract

If a set of charged objects collide in space and the fragments disperse, then this process will emit electromagnetic waves. Classical soft photon theorem determines the constant term and the leading power law fall-off of the wave-form at late and early times in terms of only the momenta and charges of the incoming and outgoing objects. In this paper we determine an infinite set of subleading terms in the late and early time expansion of the wave-form, which also depend only on the momenta and charges of the incoming and outgoing particles. For two-particle scattering, we derive a resummed low-frequency electromagnetic wave-form, as well as the resummed wave-form at early and late times. In this analysis we ignore the effect of long range gravitational interaction, but our result is unaffected by any other short range interactions among the objects.