Enhanced Binding in non-relativistic QED

TL;DR

This paper demonstrates that in non-relativistic QED, a spinless particle can have a ground state even without eigenvalues in the Schrödinger operator, under small coupling conditions.

Contribution

It proves the existence of a ground state in the Pauli-Fierz model when the Schrödinger operator lacks eigenvalues, highlighting a novel aspect of binding in quantum electrodynamics.

Findings

Ground state exists even without Schrödinger eigenvalues.

Result holds for small coupling constant.

Applicable to spinless particles in non-relativistic QED.

Abstract

We consider a spinless particle coupled to a photon field and prove that even if the Schr\"odinger operator $p^2 + V$ does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant $\alpha$ is small.