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arXiv · math-ph/0108027

Three dimensional quadratic algebras: Some realizations and representations

V. Sunil Kumar·B. A. Bambah·R. Jagannathan
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Abstract

Four classes of three dimensional quadratic algebras of the type $\lsb Q_0 , Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb Q_+ , Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$, where $(a,b,c)$ are constants or central elements of the algebra, are constructed using a generalization of the well known two-mode bosonic realizations of $su(2)$ and $su(1,1)$. The resulting matrix representations and single variable differential operator realizations are obtained. Some remarks on the mathematical and physical relevance of such algebras are given.

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V. Sunil Kumar, B. A. Bambah, R. Jagannathan. 2001-08-31. Three dimensional quadratic algebras: Some realizations and representations. https://doi.org/10.1088/0305-4470%2F34%2F41%2F313

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