Three dimensional quadratic algebras: Some realizations and representations

Abstract

Four classes of three dimensional quadratic algebras of the type $\lsb Q_0 , Q_\pm \rsb$ $=$ $\pm Q_{\pm }$, $\lsb Q_+ , Q_- \rsb$ $=$ $a{Q}_0^2+b{Q}_0+c$, 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.

LaTeX2e, 23 pages, to appear in J. Phys. A: Math. Gen

References in corpus (1)

• Spectrum generating algebra of the C_λ-extended oscillator and multiphoton coherent states

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