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 limiting operator.
On the domain of the Nelson Hamiltonian
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abstract
The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper we study mapping properties of the Gross-transform in order to characterize regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian was well. - This work is a continuation of our previous work on the Fr\"ohlich Hamiltonian.
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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 limiting operator.