On the gauge parameter dependence of QED

The gauge parameter dependence of QED in the covariant gauge was given explicitly long time ago by Landau and Khalatnikov. We elucidate their result by giving two new derivations. The first derivation uses the BRST invariance of the theory with a Stückelberg field, which is a non-interacting fictitious Goldstone boson field. The second derivation is more straightforward but calculational.