The translation invariant massive Nelson model: I. The bottom of the spectrum
ANNALES HENRI POINCARE, vol.6, no.6, pp.1091-1135, 2005 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 6 Issue: 6
- Publication Date: 2005
- Doi Number: 10.1007/s00023-005-0234-8
- Journal Name: ANNALES HENRI POINCARE
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.1091-1135
- Dokuz Eylül University Affiliated: No
Abstract
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.