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

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.

References in corpus (6)

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• Towards asymptotic completeness of two-particle scattering in local relativistic QFT
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Cited by in corpus (7)

• On the domain of the Nelson Hamiltonian
• Monotonicity of the polaron energy II:General theory of operator monotonicity
• Towards asymptotic completeness of two-particle scattering in local relativistic QFT
• On renormalized Hamiltonian nets
• Monotonicity of the polaron energy
• On the semigroup generated by the renormalized Nelson Hamiltonian
• Differential Equations of Quantum Mechanics