Consider the Lagrangian of the Gupta-Bleuer formalism given by: $$\mathcal{L} =-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} -\frac{1}{2\xi}(\partial A)^2.$$ I understand the necessity of the gauge fixing term: Without it, we would have $\Pi^\kappa=F^{\kappa 0}$ and therefore $\Pi^0=F^{00}=0$ due to the antisymmetry of the electromagnetic tensor, resulting in a contradiction with the commutator $[A^0(t,x),\Pi^0(t,x')]=i\delta^3(x-x')$ given by canonical quantization.
The Wikipedia page of gauge fixing claims, that the Feynman gauge $\xi=1$ and the Yennie gauge $\xi=3$ are often the most useful ones for calculations. I understand this for the Feynman gauge, as for example the Gupta-Bleuer propagator is (compare with equation 4.95 here for example) given by: $$\widetilde{\Delta}_{\mathrm{GB},\mu\nu}(k) =-\frac{i}{k^2+i\epsilon}\left(\eta_{\mu\nu}+(\xi-1)\frac{k_\mu k_\nu}{k^2}\right).$$ But where is the Yennie gauge useful? So far, I have not seen an example or found one. ("Yennie" is only mentioned in eight posts in total on PSE.) What is an example or a sketch of a derivation in Gupta-Bleuer formalism or QED, where the Yennie gauge is useful, or an explanation why it is special enough to deserve its own name?
