Multiplicity of ground states in quantum field models: Applications of asymptotic fields

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Abstract

Ground states of Hamiltonian H of quantum field models are investigated. The infimum of the spectrum of H is in the edge of its essential spectrum. By means of the asymptotic field theory, we give a necessary and sufficient condition for that the expectation value of the number operator of ground states is finite, from which we give an upper bound of the multiplicity of ground states of H. Typical examples are massless GSB models and the Pauli-Fierz model with spin 1/2.

Original languageEnglish
Pages (from-to)431-470
Number of pages40
JournalJournal of Functional Analysis
Volume224
Issue number2
DOIs
Publication statusPublished - Jul 15 2005

All Science Journal Classification (ASJC) codes

  • Analysis

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