BRS differential algebras in SYM-theories

Abstract

The strong reality condition A^† = − A characterizing the gauge vector representation allows a geometric formulation of classical SYM-theories which projects without any supergauge fixing to a simple space-time theory. But, analogously to the WZ-gauge fixing in the chiral basis, this process destroys the supergeometry and in particular the mathematical structure of the BRS differential algebra ; the resulting component field algebras are necessarily field dependent.