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One-particle (improper) states in Nelson’s massless model. (English) Zbl 1057.81024

Summary: In the one-particle sector of Nelson’s massless model, the one-particle states are constructed for an arbitrarily small infrared cutoff in the interaction term of the Hamiltonian of the system. The performed method is a constructive one which exploits only regular perturbation theory, by a suitable iteration scheme. The disappearance of one-particle states is showed in the limit of no infrared regularization. Constructive features, as regularity in some parameters, are also inquired.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81T10 Model quantum field theories
81V10 Electromagnetic interaction; quantum electrodynamics
81V80 Quantum optics
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