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arXiv · hep-th/9307102

Wigner Quantum Oscillators

T. D. Palev·N. I. Stoilova
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Abstract

We present three groups of noncanonical quantum oscillators. The position and the momentum operators of each of the groups generate basic Lie superalgebras, namely $sl(1/3)$, $osp(1/6)$ and $osp(3/2)$. The $sl(1/3)$-oscillators have finite energy spectrum and finite-dimensions. The $osp(1/6)$-oscillators are related to the para-Bose statistictics. The internal angular momentum $s$ of the $osp(3/2)$-oscillators takes no more than three (half)integer values. In a particular representation $s=1/2$.

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T. D. Palev, N. I. Stoilova. 1993-07-15. Wigner Quantum Oscillators. https://doi.org/10.1088/0305-4470%2F27%2F3%2F035

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