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 Hamiltonian H(alpha) of the model with a coupling parameter alpha is an element of R acts in the tensor product H x F-b of a Hilbert space H and the boson (symmetric) Fock space F-b over L-2(R-v). The existence and uniqueness of ground stales of H(alpha) are investigated. The degeneracy of the ground states is also discussed. The results obtained are nonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy of H(alpha) as \alpha\ --> infinity is also established. (C) 1997 Academic Press.