Representations of Generalized a$_r$ Statistics and Eigenstates of Jacobson Generators

Details Representations of Generalized a$_r$ Statistics and Eigenstates of Jacobson Generators Representations of Generalized a$_r$ Statistics and Eigenstates of Jacobson Generators

2006-06-20

arxiv.org/abs/math-ph/0606051v1

Physics

Mathematical Physics

10 pages, to appear in MPLA (2006)

Scientific paper

10.1142/S0217732306019943

We investigate a generalization of $A_r$ statistics discussed recently in the literature. The explicit complete set of state vectors for the $A_r$ statistics system is given. We consider a Bargmann or an analytic function description of the Fock space corresponding to $A_r$ 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.

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