Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models

Details Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models

2001-10-26

arxiv.org/abs/hep-th/0110246v2

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 14 pages, added references and corrected some typos. To be published in Proc. of Int. Workshop ``Supersymmetries and Qu

Scientific paper

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.

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