REPRESENTATIONS OF GENERALIZED Ar STATISTICS AND EIGENSTATES OF JACOBSON GENERATORS

Abstract

We investigate a generalization of Ar statistics discussed recently in the literature. The explicit complete set of state vectors for the Ar statistics system is given. We consider a Bargmann or an analytic function description of the Fock space corresponding to Ar statistics of bosonic kind. This brings, in a natural way, the so-called Gazeau–Klauder coherent states defined as eigenstates of the Jacobson annihilation operators. The minimization of Robertson uncertainty relation is also considered.