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.
Cite
@article{arxiv.math-ph/9912024,
title = {A Fractional Supersymmetric Oscillator and Its Coherent States},
author = {Mohammed Daoud and Maurice Kibler},
journal= {arXiv preprint arXiv:math-ph/9912024},
year = {2007}
}
Comments
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