Generalized fermion algebra

Abstract

A one-parameter generalized fermion algebra ${\mathcal{B}}_{\kappa }(1)$ is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A special attention is devoted to the limiting case $\kappa \to 0$ where the fermionic coherent states, labeled by Grassmann variables, are obtained. The physical relevance of the algebra is illustrated throughout Calogero-Sutherland system.

11 pages, typos in eqs. 2 and 3 are corrected

References in corpus (2)

• Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics
• Fractional supersymmetry and hierarchy of shape invariant potentials