On the $q$-deformed oscillator algebras:$su_q(1,1)$ and $su_q(2)$

Abstract

We study the relations between $q$-deformations and $q$-coherent states of the single oscillator representations for $su_q(1,1)$ and $su_q(2)$ algebras; Dyson and Holstein-Primakoff type in terms of Biedenharn, Macfarlane and anyonic oscilators. We also discuss the related Fock-Bargmann $q$-derivative and integration.

19 pages, Revtex, no figures