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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
publication:
 
JNMP
volume-issue:   4 - 3-4
pages:   338 - 349
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.1997.4.3-4.8 (how to use a DOI)
author(s):
 
Asao ARAI
publication date:
 
September 1997
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:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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