Exterior Differentials in Superspace and Poisson Brackets of Diverse Grassmann Parities

Abstract

It is shown that two definitions for the exterior differential in superspace, giving the same exterior calculus, when applied to the Poisson bracket lead to the different results. Examples of the even and odd linear brackets, corresponding to semi-simple Lie groups, are given and their natural connection with BRST and anti-BRST charges is indicated.

arXiv comment5 pages, LATEX 2.09. The talk at the 9th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY'01, JINR, Dubna, Russia, 11-17 June, 2001). To be published in the Proceedings of this Conference. Correction of misprints