Lorentz Casimir invariants
= Lorentz Casimir invariants
The quadratic contraction $M_{\mu\nu}M^{\mu\nu}$ is parity even, while $M_{\mu\nu}\widetilde M^{\mu\nu}$ is parity odd. Their linear combinations give the quadratic Casimirs of the two chiral $\mathfrak{sl}_2$ factors.