We can identify APS as a subalgebra of the spacetime algebra (STA) C ℓ ℓ 1 , 3 ( R ) , defining σ σ k = γ γ k γ γ 0 and I = γ γ 0 γ γ 1 γ γ 2 γ γ 3 . The γ γ μ μ s have the same algebraic properties of the gamma matrices but their matrix representation is not needed. The derivative is now ∇ ∇ = γ γ μ μ ∂ ∂ μ μ .