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arXiv · 2312.08455

A perturbation theory for the Coulomb-phase infrared divergence

Luke Lippstreu
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Abstract

We construct a perturbation theory which we conjecture to be free of the Coulomb-phase infrared divergence. This perturbation theory is developed for one of the simplest yet prototypical scattering amplitudes which would otherwise exhibit this divergence: the semiclassical scattering of a spinless boson on a background Coulomb field. The perturbation theory is based upon replacing plane waves with Coulomb wavefunctions, and the free-field propagator with the Coulomb propagator, in order to appropriately match the asymptotics of the exact in/out states. We compute the leading-order (LO) and next-to-leading-order (NLO) infrared-finite scattering amplitudes in this framework, which include effects to all orders in the coupling, and demonstrate that these amplitudes are in agreement with the known exact amplitude at these orders. We comment on the Runge-Lenz symmetry of the LO amplitude, under which the states furnish a principal-series representation of the Euclidean conformal group on the 2-sphere.

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Luke Lippstreu. 2026-08-12. A perturbation theory for the Coulomb-phase infrared divergence. https://arxiv.org/abs/2312.08455

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