Bargmann Representation for Some Deformed Harmonic Oscillators with Non-Fock Representation

  • Michèle Irac-Astaud
  • Guy Rideau
Part of the CRM Series in Mathematical Physics book series (CRM)


We prove that Bargmann representations exist for some deformed harmonic oscillators that admit non-Fock representations. In specific cases, we explicitly obtain the resolution of the identity in terms of a true integral on the complex plane. We prove in explicit examples that Bargmann representations cannot always be found, particularly when the coherent states do not exist in the whole complex plane.


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© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Michèle Irac-Astaud
  • Guy Rideau

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