Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Fock type and applications to quantum field Hamiltonians

Arai, A.

Hokkaido University Preprint Series in Mathematics, 1999, 445, 1-24

Permalink : https://doi.org/10.14943/83591

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アクセス権	open access
DOI	https://doi.org/10.14943/83591
URI	https://hdl.handle.net/2115/69195
タイトル	Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Fock type and applications to quantum field Hamiltonians
著者	著者名 Arai, A.
言語	英語
キーワード	essential spectrum
	Fock space
	second quantization
	quantum field
	spmboson model
	Pauli-Fierz model
発行日	1999-02-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	445
ページ	1-24
抄録	We establish general theorems on locating the essential spectrum of a self-adjoint operator of the form A® I+ I® df(S) + Hr on the tensor product 1-{ ® Fb(K) of a Hilbert space 1-l and the abstract Boson Fack space Fb(K) over a Hilbert space K, where A is a self-adjoint operator on 1-l bounded from below, df(S) is the second quantization of a nonnegative self-adjoint operator S on K and Hr is a symmetric operator on 1-l ® Fb(K). We then apply the theorems to the generalized spin-boson model (A. Arai· and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503) and a general class of models of quantum particles coupled to a Bose field including the Pauli-Fierz model in nonrelativistic quantum electrodynamics.
資源タイプ	紀要論文
出版タイプ	Version of Record