A fractional supersymmetric oscillator and its coherent states

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 Z2-graded) supersymmetric oscillator Hamiltonian. Our Hamiltonian describes a fractional (or Zk-graded) supersymmetric oscillator for which the fractional supercoherent states are coherent states. 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.