On the construction of generalized su(1, 1) coherent states

A general approach for building coherent states associated to generalized su(1, 1) algebra is developed. The problem of completeness of these coherent states is studied for some particular cases, and the physical properties of these states are investigated through the evaluation of Mandelʹs parameter using an alteration of the Holstein–Primakoff realization of the su(1, 1) algebra. It is shown that these states exhibit sub-Poissonian, Poissonian, or super-Poissonian statistics.