Infrared Problem for the Nelson Model on Static Space-Times

Christian Gérard, Fumio Hiroshima, Annalisa Panati, Akito Suzuki

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)


    We consider the Nelson model on some static space-times and investigate the problem of existence 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 existence 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. We show that if m(x) ≥ C {pipe}x{pipe}-1 at infinity for some C > 0 then the Nelson Hamiltonian has a ground state.

    Original languageEnglish
    Pages (from-to)543-566
    Number of pages24
    JournalCommunications in Mathematical Physics
    Issue number2
    Publication statusPublished - Dec 2011

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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