Ground States for Infrared Renormalized Translation-Invariant Non-Relativistic QED

TL;DR

This paper analyzes a translation-invariant quantum electrodynamics model, performing infrared renormalization to establish the existence of ground states for the fiber Hamiltonians at low momenta.

Contribution

It introduces a method for infrared renormalization of fiber Hamiltonians in non-relativistic QED, demonstrating ground state existence for most total momenta.

Findings

Ground states exist for fiber Hamiltonians at low momenta.

Infrared renormalization removes infinite photon clouds.

Method applies to particles with or without spin.

Abstract

We consider a translation-invariant Pauli-Fierz model describing a non-relativistic charged quantum mechanical particle interacting with the quantized electromagnetic field. The charged particle may be spinless or have spin one half. We decompose the Hamiltonian with respect to the total momentum into a direct integral of so called fiber Hamiltonians. We perform an infrared renormalization, in the sense of norm resolvent convergence, for each fiber Hamiltonian, which has the physical interpretation of removing an infinite photon cloud. We show that the renormalized fiber Hamiltonians have a ground state for almost all values for the total momentum with modulus less than one.