2024-03-28T08:28:41Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/692302022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Stability of ground states in sectors and its application to the Wigner-Weisskopf modelArai, A.Hirokawa, M.Fock spaceWigner-Weisskopf modelground stateground state energystabilityconservation lawfirst excited state410We 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69230info:doi/10.14943/83626https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69230/1/pre480.pdfHokkaido University Preprint Series in Mathematics4801162000-03-01engpublisher