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.


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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