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