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

DOI

10.2991/jnmp.1997.4.3-4.8How to use a DOI?

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 Bogolyubov (canonical) transformation and a partial isometry on the Fock space of the representation.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - Asao Arai
PY  - 1997
DA  - 1997/09/01
TI  - 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
JO  - Journal of Nonlinear Mathematical Physics
SP  - 338
EP  - 349
VL  - 4
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1997.4.3-4.8
DO  - 10.2991/jnmp.1997.4.3-4.8
ID  - Arai1997
ER  -