Spectral Renormalization Group and Local Decay in the Standard Model of the Non-relativistic Quantum Electrodynamics

TL;DR

This paper establishes the limiting absorption principle for non-relativistic QED and the Nelson model using spectral renormalization group and Mourre theory, advancing understanding of electron-photon and electron-phonon interactions.

Contribution

It introduces a novel combination of spectral renormalization group and Mourre theory to analyze the spectral properties of these models.

Findings

Proves the limiting absorption principle for non-relativistic QED.

Extends the technique to the Nelson model for electron-phonon interactions.

Provides a new analytical framework for spectral analysis in quantum field models.

Abstract

We prove the limiting absorption principle for the standard model of the non-relativistic quantum electrodynamics (QED) and for the Nelson model describing interactions of electrons with phonons. To this end we use the spectral renormalization group technique on the continuous spectrum in conjunction with the Mourre theory.