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Equivalence of Light-Front and Covariant Quantum Electrodynamics at One Loop Level and the form of the Gauge Boson Propagator

We discuss the equivalence of the standard covariant expressions and light-front expressions of the three fundamental one loop Feynman diagrams of Quantum Electrodynamics viz. vertex correction, fermion self-energy and vacuum polarization in the light-front gauge obtained using time-ordered Hamiltonian perturbation theory. Although this issue has been addressed by us and others previously, our emphasis in this article is to resolve any ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We show how integrating over the light-front energy consistently in the covariant expression of each of the three one loop corrections leads to the propagating as well as the instantaneous diagrams of the light-front theory. In doing so, we re-establish the necessity of using the doubly transverse gauge boson propagator.