Due to existence of several ways to fix a gauge of aan EM field in QED, there are several ways to quantize it. That leads to non-uniqueness of photon propagator and hence to non-uniqueness of integrals corresponding to Feynman diagrams in perturbative calculations.
Presumably in calculations of physical interest, such as $S$-matrix, this non-uniqueness should not play a role and should cancel out in perturbative calculations. My question is whether there is a good place to read a proof of the latter statement?