where σ σ μ μ ν ν = i [ γ γ μ μ , γ γ ν ν ] / 2 is the angular momentum operator and ϵ ϵ i j k is the totally antisymmetric tensor. This can be brought to a slightly more recognizable form by defining the 3D spin operator Σ Σ m ≡ ≡ ϵ ϵ i j m σ σ i j , taking a plane-wave state ψ ψ ( x ) = e − − i k ⋅ ⋅ x ψ ψ ( k ) , applying the on-shell constraint that k ⋅ ⋅ k = 0 and normalizing the momentum to be a 3D unit vector: k ^ ^ i = k i / k 0 to write