### 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 language | English |
---|---|

Pages (from-to) | 513-527 |

Number of pages | 15 |

Journal | Reviews in Mathematical Physics |

Volume | 13 |

Issue number | 4 |

Publication status | Published - Apr 1 2001 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Reviews in Mathematical Physics*,

*13*(4), 513-527.

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

Research output: Contribution to journal › Article

*Reviews in Mathematical Physics*, vol. 13, no. 4, pp. 513-527.

}

TY - JOUR

T1 - Stability of ground states in sectors and its application to the Wigner-Weisskopf model

AU - Arai, Asao

AU - Hirokawa, Masao

PY - 2001/4/1

Y1 - 2001/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035635350&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035635350&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 513

EP - 527

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 4

ER -