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A class of representations of the *-algebra of the canonical commutation relations over a Hilbert space and instability of embedded eigenvalues in quantum field models
Title: | A class of representations of the *-algebra of the canonical commutation relations over a Hilbert space and instability of embedded eigenvalues in quantum field models |
Authors: | Arai, A. Browse this author |
Issue Date: | 1-Dec-1996 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 367 |
Start Page: | 1 |
End Page: | 12 |
Abstract: | In models of a quantum harmonic oscillator coupled to a quantum field with a quadratic interaction, embedded eigenvalues of the unperturbed system may be unstable under the perturbation given by the interaction of the oscillator with the quantum field. A general mathematical structure underlying this phenomenon is clarified in terms of a class of Fock space representations of the *-algebra of the canonical commutation relations over a Hilbert space. It is also shown that each of the representations is given as a composition of a proper Bogoliubov ( canonical) transformation and a partial isometry on the Fock space of the representation. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69117 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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