Off-shell nilpotence of the Yang-Mills BRST quartet
= Off-shell nilpotence of the Yang-Mills BRST quartet
{title2=$sA=Dc,\quad sc=-g(c\times c)/2,\quad s\bar c=-b,\quad sb=0$}
Using the <graded Leibniz rule>, $s^2A=D(sc)+g(Dc)\times c=0$ because $D(c\times c)=2(Dc)\times c$. The <graded Jacobi identity> gives $s^2c=g^2(c\times c)\times c/2=0$. <BRST nilpotence> on the antighost and <Nakanishi-Lautrup field> is immediate. No field equations are required.