Skip to main content

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


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.

Author information



Corresponding author

Correspondence to Alessandro Pizzo.

Additional information

Communicated by Gian Michele Graf

submitted 29/04/02, accepted: 11/10/02

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Cite this article

Pizzo, A. One-particle (improper) States in Nelson’s Massless Model . Ann. Henri Poincaré 4, 439–486 (2003).

Download citation


  • Perturbation Theory
  • Iteration Scheme
  • Regular Perturbation
  • Constructive Feature
  • Infrared Cutoff