On Rayleigh scattering in non-relativistic quantum electrodynamics

TL;DR

This paper details the proofs of key results in non-relativistic quantum electrodynamics, focusing on Rayleigh scattering and asymptotic completeness for photon and phonon states at energies below ionization.

Contribution

It provides rigorous proofs of asymptotic completeness and bounds on photon/phonon growth in non-relativistic QED, extending previous results with detailed mathematical justifications.

Findings

Established lower bounds on photon/phonon distance growth

Proved asymptotic completeness for Rayleigh scattering states

Extended results to phonon cases with detailed proofs

Abstract

In this note we provide details of the proofs of the main results of our paper [19] to the standard model of non-relativistic quantum electrodynamics in which particles are minimally coupled to the quantized electromagnetic field at energies below the ionization threshold. Recall that in [19] we proved several lower bounds on the growth of the distance of the escaping photons/phonons to the particle system. Using some of these results, we proved asymptotic completeness (for Rayleigh scattering) on the states for which the expectation of the photon/phonon number is bounded uniformly in time. However, we provided details only for the phonon case.