Infrared catastrophe for Nelson's model - Non-existence of ground state and soft-boson divergence

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Abstract

We mathematically study the infrared catastrophe for the Hamiltonian of Nelson's model when it has the external potential in a general class. For the model, we prove the pull-through formula on ground states in operator theory first. Based on this formula, we show both non-existence of any ground state and divergence of the total number of soft bosons.

Original languageEnglish
Pages (from-to)897-922
Number of pages26
JournalPublications of the Research Institute for Mathematical Sciences
Volume42
Issue number4
DOIs
Publication statusPublished - Dec 1 2006
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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