On the domain of the Nelson Hamiltonian

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 Fröhlich Hamiltonian.

25 pages, no figures

References in corpus (2)

• Coulomb scattering in the massless Nelson model III. Ground state wave functions and non-commutative recurrence relations
• The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold

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