The translation invariant massive Nelson model: I. The bottom of the spectrum

Moller J.

ANNALES HENRI POINCARE, vol.6, no.6, pp.1091-1135, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 6
  • Publication Date: 2005
  • Doi Number: 10.1007/s00023-005-0234-8
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1091-1135
  • Dokuz Eylül University Affiliated: No


In this paper we analyze the bottom of the energy-momentum spectrum of the translation invariant Nelson model, describing one electron linearly coupled to a second quantized massive scalar field. Our results are valid for all values of the coupling constant and include an HVZ theorem, non-degeneracy of ground states, existence of isolated groundstates in dimensions 1 and 2, non-existence of ground states embedded in the bottom of the essential spectrum in dimensions 3 and 4, (i.e., at total momenta where no isolated groundstate eigenvalue exists), and we study regularity and monotonicity properties of the bottom of the essential spectrum, as a function of total momentum.