Asao Arai, Masao Hirokawa
Ground States of a General Class of Quantum Field Hamiltonians
(127K, LATeX 2e)
ABSTRACT. We consider a model of a quantum mechanical
system coupled to a (massless) Bose field,
called the generalized spin-boson model
(A. Arai and M. Hirokawa, J. Funct. Anal.
{\bf 151} (1997), 455--503),
{\it without infrared regularity condition}.
We define a regularized Hamiltonian $H(\nu)$ with a
parameter $\nu \geq 0$ such that $H=H(0)$ is the Hamiltonian
of the original model. We clarify a relation
between ground states of $H(\nu)$ and those of $H$ by
formulating sufficient conditions under which weak limits,
as $\nu \to 0$, of the ground states of $H(\nu)$'s are those of $H$.
We also establish existence theorems on ground states of $H(\nu)$
and $H$ under weaker conditions than in the previous paper
mentioned above.