Lie superalgebraic approach to quantum statistics : osp(3|2) Wigner quantum oscillator

The ordinary Bose and Fermi statistics and their generalizations para-Bose and para-Fermi statistics are considered from an algebraic point of view. It is indicated that they correspond to representations of Lie superalgebras B(0|n) and Bn. Generalized statistics and nonstandard quantum systems associated to the other basic classical Lie superalgebras are discussed. The Wigner quantum oscillator corresponding to the Lie superalgebra osp(3|2) is considered.

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