Ground State and Resonances in the Standard Model of Non-relativistic QED

TL;DR

This paper proves the existence of ground states and resonances in non-relativistic QED using a novel canonical transformation and spectral renormalization group methods.

Contribution

It introduces a new canonical transformation and Banach space framework to analyze the spectral properties of QED Hamiltonians.

Findings

Existence of ground states established.

Resonances in the standard non-relativistic QED model demonstrated.

New analytical techniques developed for spectral analysis.

Abstract

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.