On the domain of the Nelson Hamiltonian
Mathematical Physics
2018-05-23 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1711.10916,
title = {On the domain of the Nelson Hamiltonian},
author = {Marcel Griesemer and Andreas Wünsch},
journal= {arXiv preprint arXiv:1711.10916},
year = {2018}
}
Comments
25 pages, no figures