One-particle (improper) States in Nelson’s Massless Model

Abstract.

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.