On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

Details On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

2001-01-08

arxiv.org/abs/math-ph/0101009v1

Physics

Mathematical Physics

14 pages, LaTex file. Paper written from a lecture presented (by M.R.K.) at the Sixth International School on Theoretical Phys

Scientific paper

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.

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