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arXiv · hep-th/9307083

Complex analytic realizations for quantum algebras

J. A. de Azcárraga·Demosthenes Ellinas
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Abstract

A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for the cases of the $q$-oscillators ($q$-Weyl-Heisenberg algebra) and for the $su_{q}(2)$ and $su_{q}(1,1)$ algebras and their co-products. They are given in terms of a series in powers of ordinary derivative operators which act on the Bargmann-Hilbert space of functions endowed with the usual integration measure. In the $q\rightarrow 1$ limit these realizations reduce to the usual analytic Bargmann realizations for the three algebras.

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J. A. de Azcárraga, Demosthenes Ellinas. 1993-07-12. Complex analytic realizations for quantum algebras. https://doi.org/10.1063/1.530591

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