with ψ ψ L ∗ ∗ ( x ) the complex conjugate of ψ ψ L ( x ) . The subscript L is used throughout this section to denote a left -handed chiral spinor; under a parity transformation, this can be taken to a right-handed spinor, and so one also has a right-handed form of the equation. This applies to the four-component equation as well; further details are presented below.