Wigner Quantum Oscillators

Details Wigner Quantum Oscillators Wigner Quantum Oscillators

1993-07-15

arxiv.org/abs/hep-th/9307102v1

J.Phys. A27 (1994) 977-984

Physics

High Energy Physics

High Energy Physics - Theory

8 pagex, TeX, IC/93/190

Scientific paper

10.1088/0305-4470/27/3/035

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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