Absence of ground state for the Nelson model on static space-times

C. Gérard, F. Hiroshima, A. Panati, A. Suzuki

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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)≤Cx at infinity for some C>0 and μ>1 then the Nelson Hamiltonian has no ground state.

Original languageEnglish
Pages (from-to)273-299
Number of pages27
JournalJournal of Functional Analysis
Volume262
Issue number1
DOIs
Publication statusPublished - Jan 1 2012

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All Science Journal Classification (ASJC) codes

  • Analysis

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