Ground states of a general class of quantum field Hamiltonians

We consider a model of a quantum mechanical system coupled to a (massless) Bose field, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503), without infrared regularity condition. We define a regularized Hamiltonian H(v) with a parameter v greater than or equal to 0 such that H = H(0) is the Hamiltonian of the original model. We clarify a relation between ground states of H(v) and those of H by formulating sufficient conditions under which weak limits, as v --> 0, of the ground states of H(v)'s are those of H. We also establish existence theorems on ground states of H(v) and H under weaker conditions than in the previous paper mentioned above.