= Solution
The <covariant Landau gauge> is the zero-parameter limit $\xi\to0$ of the covariant gauge family. It imposes the <Lorenz gauge> condition $\partial_\mu A^\mu=0$ sharply. The <Landau gauge photon propagator> is the transverse part of the inverse from <c/solution>:
$$
\boxed{D^{\rm L}_{\mu\nu}(k)=\frac{-i}{k^2+i0}\left(\eta_{\mu\nu}-\frac{k_\mu k_\nu}{k^2}\right)}.
$$
Away from the pole, $k^\mu D^{\rm L}_{\mu\nu}=0$, matching the divergence-free condition. This is transversality to the <four-momentum>, rather than a projector onto only the two physical spatial photon polarizations. The <Lorenz gauge> equation alone still admits residual <gauge transformations> with $\Box\chi=0$; boundary conditions and the pole prescription complete the propagator choice. The parameter limit specifies the Landau propagator without trying to invert the ungauged Maxwell operator on its longitudinal null space.
Back to article page
