Wojciech Dybalski, Jacob Schach Møller
This paper is concerned with the problem of proving asymptotic completeness for a class of translation invariant models describing a single quantum particle (the electron) linearly coupled to a massive scalar field (bosons). Our approach, which is based on a recently established Mourre estimate for these models, yields asymptotic completeness in an energy-momentum regime describing scattering of dressed particles and single asymptotic bosons. We impose no number cutoff, no restriction on the particle-field coupling strength, and no restriction on the magnitude of total momentum. Energy, however, is restricted to be below the threshold for energetic support of incoming/outgoing states containing more than one boson. The class of models we consider include the UV-cutoff Nelson and polaron models.
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http://arxiv.org/abs/1210.6645
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