A Fractional Supersymmetric Oscillator and Its Coherent States

Abstract

We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and a k-fermion leads to a definition of fractional supercoherent states. Such states involve bosonic coherent states and k-fermionic coherent states. We construct an Hamiltonian which generalizes the ordinary (or Z_2-graded) supersymmetric oscillator Hamiltonian. Our Hamiltonian describes a fractional (or Z_k-graded) supersymmetric oscillator for which the fractional supercoherent states are coherent states.

15 pages, Latex file. Paper written from a plenary talk presented (by M.K.) at the ``Sixth International Wigner Symposium'', Istanbul (Turkey), 16- 22 August 1999. Submitted for publication in Turkish Journal of Physics

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