A Parafermion Generalization of Poincaré Supersymmetry

Abstract

The space-time Poincare algebra is extended by introducing a four-spinor generator whose components satisfy certain trilinear parafermi commutation relations. The spin content of the irreducible multiplets is analysed in the massive and massless cases, and weight diagrams constructed, for arbitrary order p of the parastatistics. The supersymmetry algebra of Wess and Zumino, and of Salam and Strathdee, is exhibited as the special case of order p = 1 in this formulation.