|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Essential spectrum of a self-adjoint operator on an abstract Hilbert space of Fock type and applications to quantum field Hamiltonians
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
|
