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Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
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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.
Forward citations
Cited by 2 Pith papers
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On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model
Infrared-divergent spin boson model loses its ground state above a finite critical coupling, proved via long range order in a dual continuum Ising model.
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Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions
The paper proves that generalized spin-boson models with normal or 2-nilpotent interactions can be ultraviolet renormalized, with norm resolvent convergence of the regularized Hamiltonians to an explicitly constructed...
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