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 H amiltonian 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 dege neracy of the ground states is also discussed. The results obtained ar e nonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula fo r the ground state energy of H(alpha) as \alpha\ --> infinity is also established. (C) 1997 Academic Press.