English

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}
}