Transverse projection operator
= Transverse projection operator
For a nonnull vector $k$ in a space with a nondegenerate bilinear form, $P_{\mu\nu}=\eta_{\mu\nu}-k_\mu k_\nu/k^2$ projects onto the subspace transverse to $k$. It obeys $P_{\mu\nu}k^\nu=0$ and $P^2=P$.