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arXiv: 1012.2655

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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 Physics Mathematics/Mathematical Physics Mathematics/Analysis of PDEs

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From: Christian Gérard <>

Submitted on: Wednesday, 8 December 2010 14:06:29

Updated on: Tuesday, 4 October 2011 19:19:08