Annales Henri Poincaré

, Volume 16, Issue 11, pp 2603–2693 | Cite as

The Translation Invariant Massive Nelson Model: III. Asymptotic Completeness Below the Two-Boson Threshold

  • Wojciech DybalskiEmail author
  • Jacob Schach Møller


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 includes the UV-cutoff Nelson and polaron models. Although this paper is a part of a larger investigation, the presentation is self-contained.


Wave Operator Asymptotic Completeness Nelson Model Propagation Observable Polaron Model 
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© Springer Basel 2014

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenGarchingGermany
  2. 2.Department of MathematicsAarhus UniversityAarhusDenmark

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