Abstract
Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian.
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Ammari, Z. Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model. Mathematical Physics, Analysis and Geometry 3, 217–285 (2000). https://doi.org/10.1023/A:1011408618527
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DOI: https://doi.org/10.1023/A:1011408618527