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

Abstract

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.

10 pages, to appear in MPLA (2006)

References in corpus (1)

• Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics

Cited by in corpus (1)

• Chiral bosons on Bargmann space associated with A${}_r$ Statistics