Representations and Properties of Generalized $A_r$ Statistics, Coherent States and Robertson Uncertainty Relations

Abstract

The generalization of $A_r$ statistics, including bosonic and fermionic sectors, is performed by means of the so-called Jacobson generators. The corresponding Fock spaces are constructed. The Bargmann representations are also considered. For the bosonic $A_r$ statistics, two inequivalent Bargmann realizations are developed. The first (resp. second) realization induces, in a natural way, coherent states recognized as Gazeau-Klauder (resp. Klauder-Perelomov) ones. In the fermionic case, the Bargamnn realization leads to the Klauder-Perelomov coherent states. For each considered realization, the inner product of two analytic functions is defined in respect to a measure explicitly computed. The Jacobson generators are realized as differential operators. It is shown that the obtained coherent states minimize the Robertson-Schrödinger uncertainty relation.

16 pages, published in JPA

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• Quantum Hall Effect in Higher Dimensions
• Coherent States for the Hydrogen Atom
• Black Hole Statistics
• The effective action for edge states in higher dimensional quantum Hall systems
• Robertson Intelligent States
• Statistical Mechanics of $qp$-Bosons in $D$ Dimensions
• Quantum Hall Effect on Higher Dimensional Spaces
• Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics

Cited by in corpus (5)

• A volume inequality for quantum Fisher information and the uncertainty principle
• Chiral bosons on Bargmann space associated with A${}_r$ Statistics
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Electromagnetic Excitations of A_n Quantum Hall Droplets
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space