It is conventional to define a pair of projection matrices Λ Λ + and Λ Λ − − , that project out the positive and negative energy eigenstates. Given a fixed Lorentz coordinate frame (i.e. a fixed momentum), these are Λ Λ + ( p ) = ∑ ∑ s = 1 , 2 u p ( s ) ⊗ ⊗ u ¯ ¯ p ( s ) = p / + m 2 m Λ Λ − − ( p ) = − − ∑ ∑ s = 1 , 2 v p ( s ) ⊗ ⊗ v ¯ ¯ p ( s ) = − − p / + m 2 m