This, in turn leads to the two compatibility conditions [ S 1 , S 2 ] ψ ψ = 0 , and [ S 1 , S 2 ] ψ ψ = 0 , provided that Δ Δ = Δ Δ ( x ⊥ ⊥ ) . These compatibility conditions do not restrict the gamma matrix structure of Δ Δ . That matrix structure is determined by the type of vertex-vertex structure incorporated in the interaction. For the two types of invariant interactions Δ Δ emphasized in this article they are Δ Δ L ( x ⊥ ⊥ ) = − − 1 1 1 2 L ( x ⊥ ⊥ ) 2 O 1 , scalar , Δ Δ G ( x ⊥ ⊥ ) = γ γ 1 ⋅ ⋅ γ γ 2 G ( x ⊥ ⊥ ) 2 O 1 , vector , O 1 = − − γ γ 51 γ γ 52 .