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

Arai, A.

Hokkaido University Preprint Series in Mathematics, 1996, 367, 1-12

Permalink : https://doi.org/10.14943/83513

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DOI	https://doi.org/10.14943/83513
URI	https://hdl.handle.net/2115/69117
タイトル	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
著者	著者名 Arai, A.
言語	英語
発行日	1996-12-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	367
ページ	1-12
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record