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A Deformed Bargmann Transform by an SU(2) Matrix Parameter

Allal Ghanmi

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The Laguerre 2D polynomials depending on an arbitrary \nmatrix Q in SU(2) as a fixed parameter are used to construct a set of \ncoherent states. The corresponding coherent state transforms constitute \na deformation by matrix Q of a generalized Bargmann transform.

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(q;l,lambda)(q;l,\\lambda)(q;l,lambda)-Deformed Heisenberg Algebra: Coherent States, Their Statistics and Geometry
The Heisenberg algebra is deformed with the set of parameters q,l,lambda\\{q, l,\\lambda\\}q,l,lambda to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the subPoissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.