  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.
