4461 articles – 13151 references  [version française]
 HAL: hal-00544552, version 1
 arXiv: 1012.2655
 Absence of ground state for the Nelson model on static space-times
 Christian Gérard 1, Fumio Hiroshima 2, Annalisa Panati 3, 4, A. Suzuki 5
 (2010-12-08)
 We consider the Nelson model on some static space-times and investigate the problem of absence of a ground state. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. We investigate the absence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass $m(x)$ tends to $0$ at spatial infinity. Using path space techniques, we show that if $m(x)\leq C |x|^{-\mu}$ at infinity for some $C>0$ and $\mu>1$ then the Nelson Hamiltonian has no ground state.
 1: Laboratoire de Mathématiques d'Orsay (LM-Orsay) CNRS : UMR8628 – Université Paris XI - Paris Sud 2: Department of Mathematics University of Kyushu 3: Département de Mathématiques (DP) Université Sud Toulon Var 4: Centre de Physique Théorique (CPT) CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var 5: Departement of Materials Science and Engineering Iwate university
 Subject : Physics/Mathematical PhysicsMathematics/Mathematical PhysicsMathematics/Analysis of PDEs
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 hal-00544552, version 1 http://hal.archives-ouvertes.fr/hal-00544552 oai:hal.archives-ouvertes.fr:hal-00544552 From: Christian Gérard <> Submitted on: Wednesday, 8 December 2010 14:06:29 Updated on: Tuesday, 4 October 2011 19:19:08