Asao Arai, Masao Hirokawa
Stability of Ground States in Sectors
and Its Application to the Wigner-Weisskopf Model.
(42K, LATeX 2e)
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.