Wigner Quantum Oscillators

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 $s=1/2$.

8 pagex, TeX, IC/93/190

Cited by in corpus (8)

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• Many-Body Wigner Quantum Systems
• Para-Statistics as Lie-super Triple Systems
• Wigner quantum oscillators. Osp(3/2) oscillators
• Representations of the Lie Superalgebra gl(1|n) in a Gel'fand-Zetlin Basis and Wigner Quantum Oscillators
• Exclusion statistics,operator algebras and Fock space representations
• Unification of parastatistics defined as triple operator algebras
• Highest weight irreducible representations of the Lie superalgebra $gl(1/\infty )$