| Stability of Ground States in Sectors and Its Application to the Wigner-Weisskopf Model (1999) | |||||||||||||||
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. | |||||||||||||||
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