Polynomial deformations of $osp(1/2)$ and generalized parabosons

Details Polynomial deformations of $osp(1/2)$ and generalized parabosons Polynomial deformations of $osp(1/2)$ and generalized parabosons

1994-10-20

arxiv.org/abs/hep-th/9410145v1

J.Math.Phys. 36 (1995) 4507-4518

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, LaTeX, TWI-94-XX

Scientific paper

10.1063/1.530904

We consider the algebra $R$ generated by three elements $A,B,H$ subject to three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we speak of polynomial deformations of $osp(1/2)$. Irreducible representations of $R$ are described, and in the case $\deg(f)\leq 2$ we obtain a complete classification, showing some similarities but also some interesting differences with the usual $osp(1/2)$ representations. The relation with deformed oscillator algebras is discussed, leading to the interpretation of $R$ as a generalized paraboson algebra.

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