On the existence and uniqueness of ground states of a generalized spin-boson model

A generalization of the standard spin-boson model is considered. The HamiltonianH(α) of the model with a coupling parameterα∈Racts in the tensor product H⊕F_bof a Hilbert space H and the boson (symmetric) Fock space F_boverL²(R^ν). The existence and uniqueness of ground states ofH(α) are investigated. The degeneracy of the ground states is also discussed. The results obtained arenonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy ofH(α) as |α|→∞ is also established.