Existence and non existence of a ground state for the massless Nelson model under binding condition

Abstract

We consider a model describing $N$ non-relativistic particles coupled to a massless quantum scalar field, called \emph{Nelson model}, under a binding condition on the external potential. We prove that this model does not admit ground state in the Fock representation of the canonical commutation relations, but it does in another not unitarily equivalent coherent representation. Remark that the binding condition is satisfied for small values of the coupling constant.

revised version

References in corpus (1)

• Infrared Catastrophe for Nelson's Model

Cited by in corpus (1)

• On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field