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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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83513

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
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

Submitter: 数学紀要登録作業用

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