The normalization chosen here is such that the scalar invariant ψ ψ ¯ ¯ ψ ψ really is invariant in all Lorentz frames. Specifically, this means u ¯ ¯ ( a ) ( p ) u ( b ) ( p ) = δ δ a b u ¯ ¯ ( a ) ( p ) v ( b ) ( p ) = 0 v ¯ ¯ ( a ) ( p ) v ( b ) ( p ) = − − δ δ a b v ¯ ¯ ( a ) ( p ) u ( b ) ( p ) = 0