All-multiplicity amplitudes in impulsive PP-waves from the worldline formalism
arxiv(2024)
摘要
We use the worldline formalism to derive Bern-Kosower type Master Formulae
for the tree-level scattering of a charged particle and an arbitrary number of
photons on impulsive PP-waves, where the coupling of the PP-wave to matter is
treated fully non-perturbatively. We show that, in a certain kinematic regime
characterised by a semi-classical positive energy condition, both off-shell
currents and scattering amplitudes exhibit two novel factorisation structures.
First, they may be written as currents in vacuum but with a single additional
photon, averaged over the momentum of that photon. This converts the all-orders
interaction with the PP-wave into a single effective interaction. Second, the
currents and amplitudes may be written as a weighted average of the
corresponding quantities in an impulsive plane wave background, with the
average taken over all possible field strengths of the plane wave. This
generalises a known single-photon result to arbitrary multiplicity.
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