Right-acting BRST differential ($Q_R$)

A right-acting BRST differential obeys the right graded Leibniz rule. This convention permits $Q\varphi =[c,\varphi ]$ together with $Qc=-[c,c]/2$. Using a left graded Leibniz rule with those same two signs does not give a nilpotent operator; one of the signs must change.