99-179 Asao Arai, Masao Hirokawa

Ground States of a General Class of Quantum Field Hamiltonians (127K, LATeX 2e) May 17, 99

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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.

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