Complex analytic realizations for quantum algebras

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 $s{u}_q(2)$ and $s{u}_q(1,1)$ 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 $q\to 1$ limit these realizations reduce to the usual analytic Bargmann realizations for the three algebras.

18 pages