Representations of Generalized aᵣ Statistics and Eigenstates of Jacobson Generators

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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.