Volume 4, Issue 3-4, September 1997, Pages 338 - 349
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
Asao Arai
Corresponding Author
Asao Arai
Available Online 1 September 1997.
- 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/).
Cite this article
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 -