The No-Binding Regime of the Pauli-Fierz Model

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 ${\alpha }_{+}-{\alpha }_{-}<\delta$.

18 pages and 1 figure

Cited by in corpus (2)

• On enhanced binding and related effects in the non- and semi-relativistic Pauli-Fierz models
• Enhanced binding of an N-particle system interacting with a scalar field II.Relativistic version