The Gauge-Field Propagator in Light-Cone Gauge: Which is the Correct One?

In the literature one can find two different expressions for the gauge-field propagator in light-cone gauge, containing the sum of three rather than two terms. The question of which of the two is the correct one has been a subject of debate. We propose a solution to this question by evaluating one-loop level processes in QED, both in the covariant approach in the light-cone gauge and in the light-front time-ordered perturbation theory (TOPT) approach, proving the equivalence between the two formulations of the theory. The form of the propagator turns out to be crucial in the proof, in particular as concerns its relation with the diagrams containing instantaneously propagating photons and instantaneous interactions. We show that the diagrams in light-front TOPT with instantaneous photons can be recovered in the covariant approach starting from the propagators with only two terms. Our proof of the equivalence clarifies which form should be used for the gauge-field propagator in the covariant approach. This result naturally applies to the QCD case also.