The translation invariant massive Nelson model: III. Asymptotic completeness below the two-boson threshold

TL;DR

This paper proves asymptotic completeness for a class of translation invariant quantum models involving an electron and a massive scalar field, specifically below the two-boson threshold, using Mourre estimates without cutoffs or coupling restrictions.

Contribution

It establishes asymptotic completeness for the massive Nelson model below the two-boson threshold without imposing cutoffs or coupling restrictions, extending previous results.

Findings

Proves asymptotic completeness for the model below the two-boson threshold.

Uses Mourre estimates to avoid cutoffs and coupling restrictions.

Includes models like UV-cutoff Nelson and polaron models.

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.