The No-Binding Regime of the Pauli-Fierz Model

Abstract

The Pauli-Fierz model $H(α)$ 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 $0<α_-< α_+$ such that $H(α)$ has no ground state for $|α|<α_-$, which complements an earlier result stating that there is a ground state for $|α| > α_+$. We develop a suitable extension of the Birman-Schwinger argument. Moreover for any given $δ>0$ examples of potentials $V$ are provided such that $α_+-α_-<δ$.

18 pages and 1 figure