The No-Binding Regime of the Pauli-Fierz Model

TL;DR

This paper investigates the absence of ground states in the Pauli-Fierz model within a specific coupling regime, providing bounds on the coupling constant and extending analytical methods in quantum electrodynamics.

Contribution

It establishes the existence of a no-binding regime for the Pauli-Fierz model and refines the understanding of ground state conditions using an extended Birman-Schwinger argument.

Findings

Existence of constants <\u0014+ such that no ground state exists for ||<-

Extension of the Birman-Schwinger argument to this context

Examples showing the gap + - - can be made arbitrarily small

Abstract

The Pauli-Fierz model $H(\alpha)$ in nonrelativistic quantum electrodynamics is considered. The external potential $V$ is sufficiently shallow and the dipole approximation is assumed. It is proven that there exist constants $0<\alpha_-< \alpha_+$ such that $H(\alpha)$ has no ground state for $|\alpha|<\alpha_-$, which complements an earlier result stating that there is a ground state for $|\alpha| > \alpha_+$. We develop a suitable extension of the Birman-Schwinger argument. Moreover for any given $\delta>0$ examples of potentials $V$ are provided such that $\alpha_+-\alpha_-<\delta$.