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We provide a rigorous construction of a large class of generalized spin-bosonmodels with ultraviolet-divergent form factors. This class comprises variousmodels of many possibly non-identical atoms with arbitrary but finite numbersof levels, interacting with a boson field. Ultraviolet divergences are assumedto be mild, such that no self-energy renormalization is necessary. Ourconstruction is based on recent results by A. Posilicano, which also allow usto state an explicit formula for the domain of self-adjointness for ourHamiltonians.

Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences