The translation invariant massive Nelson model: III. Asymptotic completeness below the two-boson threshold
Mathematical Physics
2015-12-02 v2 math.MP
Abstract
We show asymptotic completeness of two-body scattering for a class of translation invariant models describing a single quantum particle (the electron) linearly coupled to a massive scalar field (bosons). Our proof is based on a recently established Mourre estimate for these models. In contrast to previous approaches, it requires no number cutoff, no restriction on the particle-field coupling strength, and no restriction on the magnitude of total momentum. Energy, however, is restricted by the two-boson threshold, admitting only scattering of a dressed electron and a single asymptotic boson. The class of models we consider include the UV-cutoff Nelson and polaron models.
Keywords
Cite
@article{arxiv.1210.6645,
title = {The translation invariant massive Nelson model: III. Asymptotic completeness below the two-boson threshold},
author = {Wojciech Dybalski and Jacob Schach Møller},
journal= {arXiv preprint arXiv:1210.6645},
year = {2015}
}