Asymptotic Electromagnetic Fields in Non-relativistic QED: the Problem of Existence Revisited

TL;DR

This paper proves the existence of scattering states with multiple high-energy photons in non-relativistic QED models, addressing a longstanding problem in the mathematical understanding of photon-electron interactions.

Contribution

It establishes the existence of multi-photon scattering states without energy restrictions, advancing the mathematical theory of non-relativistic quantum electrodynamics.

Findings

Existence of scattering states with arbitrary photon numbers.

No upper bounds on photon energies needed for multiple photons.

Addresses previous limitations in non-relativistic QED models.

Abstract

This paper is devoted to the scattering of photons at electrons in models of non-relativistic quantum mechanical particles coupled minimally to the soft modes of the quantized electromagnetic field. We prove existence of scattering states involving an arbitrary number of asymptotic photons of arbitrarily high energy. Previously, upper bounds on the photon energies seemed necessary in the case of $n>1$ asymptotic photons and non-confined, non-relativistic charged particles.