 00240 Asao Arai, Masao Hirokawa
 Stability of Ground States in Sectors
and Its Application to the WignerWeisskopf Model.
(42K, LATeX 2e)
May 23, 00

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Abstract. We consider two kinds of stability (under
a perturbation) of the ground state of
a selfadjoint 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 WignerWeisskopf 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 WignerWeisskopf model
has degenerate ground states ;
(b) for a value of the coupling constant,
the WignerWeisskopf model
has a first excited state
with energy level below the bottom of
the essential spectrum.
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