Left-acting BRST differential
= Left-acting BRST differential
{title2=$s(UV)=(sU)V+(-1)^{|U|}U(sV),\quad s^2=0$}
Writing a transformation as $\delta\Phi=\epsilon s\Phi$ with the odd parameter on the left defines this graded derivation convention. For Yang-Mills fields, $sA=Dc$, $sc=-[c,c]/2$, $sb=h$, and $sh=0$. The <Jacobi identity> supplies nilpotence; the placement of the odd parameter controls signs in a <Noether current>.