Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models
High Energy Physics - Theory
2007-05-23 v2
Abstract
It is shown that the fermionic Heisenberg-Weyl algebra with 2N=D fermionic generators is equivalent to the generalized Grassmann algebra with two fractional generators. The 2,3 and 4 dimensional Heisenberg - Weyl algebra is explicitly given in terms of the fractional generators. These algebras are used for the formulation of the N=2,3,4 extended supersymmetry. As an example we reformulate the Lax approach of the supersymmetric Korteweg - de Vries equation in terms of the generators of the generalized Grassmann algebra.
Keywords
Cite
@article{arxiv.hep-th/0110246,
title = {Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models},
author = {A. P. Isaev and Z. Popowicz and O. Santillan},
journal= {arXiv preprint arXiv:hep-th/0110246},
year = {2007}
}
Comments
LaTeX, 14 pages, added references and corrected some typos. To be published in Proc. of Int. Workshop ``Supersymmetries and Quantum Symmetries'', Sept. 21-25, 2001, Karpacz, Poland