Longitudinal gauge propagator contraction ($p^a{G}_{ab}=\xi p_b/p^2$)

For the positive-sign covariant gauge-fixing inverse, $p^a{G}_{ab}=\xi p_b/p^2$. It is not identically zero for fixed $\xi \ne 0$ and is a nonzero vector at a nonzero non-null four-momentum. Null momenta require the chosen pole prescription, and individual zero components are possible. The Landau gauge limit suppresses this longitudinal part. The Ward identity removes longitudinal contributions from physical conserved-current amplitudes.