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 suq(2) and suq(1,1) algebras and their coproducts. 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 measures. In the q→1 limit these realizations reduce to the usual analytic Bargmann realizations for the three algebras.