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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83591

Title: Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Fock type and applications to quantum field Hamiltonians
Authors: Arai, A. Browse this author
Keywords: essential spectrum
Fock space
second quantization
quantum field
spm­boson model
Pauli-Fierz model
Issue Date: 1-Feb-1999
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 445
Start Page: 1
End Page: 24
Abstract: 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69195
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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