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On the domain of the Nelson Hamiltonian
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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.
Forward citations
Cited by 2 Pith papers
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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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On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups
For negative coupling, the renormalized non-relativistic and semi-relativistic Nelson semigroups are positivity improving with respect to the Fröhlich cone at every total momentum, proven via Feynman-Kac functional in...
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