Complex analytic realizations for quantum algebras

Details Complex analytic realizations for quantum algebras Complex analytic realizations for quantum algebras

1993-07-12

arxiv.org/abs/hep-th/9307083v1

J.Math.Phys. 35 (1994) 1322-1333

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1063/1.530591

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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