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Jordan-Schwinger realizations of three-dimensional polynomial algebras

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

A three-dimensional polynomial algebra of order $m$ is defined by the commutation relations $[P_0, P_\pm]$ $=$ $\pm P_\pm$, $[P_+, P_-]$ $=$ $ϕ^{(m)}(P_0)$ where $ϕ^{(m)}(P_0)$ is an $m$-th order polynomial in $P_0$ with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders $l$ and $m$ can be combined to give two distinct $(l+m+1)$-th order polynomial algebras. This procedure follows from a generalization of the well known Jordan-Schwinger method of construction of $su(2)$ and $su(1,1)$ algebras from two mutually commuting boson algebras.

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V. Sunil Kumar, B. A. Bambah, R. Jagannathan. 2002-05-03. Jordan-Schwinger realizations of three-dimensional polynomial algebras. https://doi.org/10.1142/s0217732302007454

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