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Stability of Ground States in Sectors and Its Application to the Wigner-Weisskopf Model
| Title: | Stability of Ground States in Sectors and Its Application to the Wigner-Weisskopf Model |
| Authors: | Arai, Asao Browse this author →KAKEN DB | | Hirokawa, Masao Browse this author |
| Keywords: | Fock space | | Wigner-Weisskopf model | | ground state | | ground state energy | | stability | | conservation law | | first excited state | | MSC=81Q10 | | MSC=47B25 | | MSC=47N50 |
| Issue Date: | Apr-2001 |
| Publisher: | World Scientific Publishing Company |
| Journal Title: | Reviews in Mathematical Physics |
| Volume: | 13 |
| Issue: | 4 |
| Start Page: | 513 |
| End Page: | 528 |
| Publisher DOI: | 10.1142/S0129055X01000740 |
| Abstract: | We consider two kinds of stability (under a perturbation) of the ground state of a self-adjoint operator, being concerned with (i) the sector to which the ground state belongs and (ii) 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. |
| Rights: | Electronic version of an article published as Reviews in Mathematical Physics, Vol. 13, Issue 4, 2001, pp. 513-528, DOI: 10.1142/S0129055X01000740 © World Scientific Publishing Company, http://www.worldscinet.com/rmp/rmp.shtml |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/38266 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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