Bulg. J. Phys. vol.44 no.1 (2017), pp. 001-008



Lie Superalgebraic Approach to Quantum Statistics. osp(3|2) Wigner Quantum Oscillator

N.I. Stoilova1, J. Van der Jeugt2
1Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria
2Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Gent B-9000, Belgium
Abstract. 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 B_n. 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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