Statistical properties of the 𝒜κ<0 Weyl–Heisenberg algebra coherent states

In this paper, we study the one-parameter $\kappa$-generalized oscillator algebra ${{𝒜}}_{\kappa }$ (which includes the case of the standard Weyl–Heisenberg algebra). This algebra admits representations of finite-dimensional for negative values of the parameter $\kappa$. We construct the associated Perelomov like coherent states. We discuss their statistical properties. In particular, we derive the expressions of the Mandel parameter and Husimi function and we discuss the squeezing of the ${{𝒜}}_{\kappa }$ coherent states.