Self-adjointness and Domain of Generalized Spin–Boson Models with Mild Ultraviolet Divergences

Abstract. We provide a rigorous construction of a large class of generalized spin–boson models with ultraviolet-divergent form factors. This class comprises various models of many possibly non-identical atoms with arbitrary but finite numbers of levels, interacting with a boson field. Ultraviolet divergences are assumed to be mild, such that no self-energy renormalization is necessary. Our construction is based on recent results by A. Posilicano, which also allow us to state an explicit formula for the domain of self-adjointness for our Hamiltonians.