On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

Abstract

The Hamiltonian for a fractional supersymmetric oscillator is derived from three approaches. The first one is based on a decomposition in which a Q-uon gives rise to an ordinary boson and a k-fermion (a k-fermion being an object interpolating between boson and fermion). The second one starts from a generalized Weyl-Heisenberg algebra. Finally, the third one relies on the quantum algebra Uq(sl(2)) where q is a root of unity.

arXiv comment14 pages, LaTex file. Paper written from a lecture presented (by M.R.K.) at the Sixth International School on Theoretical Physics ``Symmetry and Structural Properties of Condensed Matter'', a school devoted to the memory of Louis Michel, Myczkowce (Poland), 31 August - 6 September 2000. To be published in ``Symmetry and Structural Properties of Condensed Matter'', eds. T. Lulek, B. Lulek and A. Wal (World Scientific, Singapore, 2001)