Stability of ground states in sectors and its application to the Wigner-Weisskopf model

Asao Arai, Masao Hirokawa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider two kinds of stability (under a perturbation) of the ground state of a self-adjoint operator: the one is concerned with the sector to which the ground state belongs and the other is about the uniqueness of the ground state. As an application to the Wigner-Weisskopf model which describes one mode fermion coupled to a quantum scalar field, we prove in the massive case the following: (a) For a value of the coupling constant, the Wigner-Weisskopf model has degenerate ground states; (b) for a value of the coupling constant, the Wigner-Weisskopf model has a first excited state with energy level below the bottom of the essential spectrum. These phenomena are nonperturbative.

Original languageEnglish
Pages (from-to)513-527
Number of pages15
JournalReviews in Mathematical Physics
Volume13
Issue number4
Publication statusPublished - Apr 1 2001
Externally publishedYes

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Ground State
Sector
sectors
ground state
Essential Spectrum
Quantum Fields
Excited States
uniqueness
Self-adjoint Operator
Energy Levels
Model
Scalar Field
Fermions
Uniqueness
fermions
energy levels
scalars
Perturbation
operators
perturbation

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Stability of ground states in sectors and its application to the Wigner-Weisskopf model. / Arai, Asao; Hirokawa, Masao.

In: Reviews in Mathematical Physics, Vol. 13, No. 4, 01.04.2001, p. 513-527.

Research output: Contribution to journalArticle

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