Above it was used several times that [ Z A , f ( Z ) ] ⋆ ⋆ = − − 2 i ∂ ∂ A f ( Z ) , ∂ ∂ A ≡ ≡ ∂ ∂ ∂ ∂ Z A , i.e. the vacuum value of the S-field acts as the derivative under the commutator. It is convenient to split the four-component Y,Z into two-component variables as Y A = ( y α α , y α α ˙ ˙ ) , Z A = ( z α α , z α α ˙ ˙ ) . Another trick that was used in the fourth equation is the invertibility of the Klein operators: