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hal-00544552, version 1

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)

Abstract: 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
  • Domain : Physics/Mathematical Physics
    Mathematics/Mathematical Physics
    Mathematics/Analysis of PDEs
 
  • 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