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Absence of Ground States in the Translation Invariant Massless Nelson Model

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  • Thomas Norman Dam

In this paper, the translation invariant massless Nelson model with ultraviolet cutoff is investigated. It is proven that the fiber operators does not have a ground state if the interaction is not infrared regular. Similar results have been obtained by other authors under severe assumptions on the regularity of the mass shell. The method introduced in this paper works under very general conditions and relies only on rotation invariance of the mass shell, non-degeneracy of ground states and the HVZ theorem.

Original languageEnglish
JournalAnnales Henri Poincare
Pages (from-to)2655-2679
Number of pages25
Publication statusPublished - 2020

    Research areas

  • Primary 81Q10, Secondary 81T10

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