Pauli-Lubanski orthogonality
= Pauli-Lubanski orthogonality
{c}
{title2=$W^\mu P_\mu=0$}
In $W^\mu=-\epsilon^{\mu\nu\rho\sigma}P_\nu M_{\rho\sigma}/2$, contracting with $P_\mu$ gives zero because the commuting momentum products are symmetric in $\mu,\nu$ while the alternating tensor is antisymmetric. Reordering $P$ and $M$ makes no difference because the resulting metric contractions with the alternating tensor vanish.
// Target: special-relativity.bigb