We consider the equivalence of covariant and light front quantum electrodynamics at one loop level. We show that the one loop expressions for fermion self-energy, vacuum polarization, and vertex correction in the covariant perturbation theory can be reduced to a sum of propagating and instantaneous diagrams of light front time-ordered perturbation theory by performing $k^{-}$ integration. We show that the third term in the doubly transverse gauge propagator is necessary to generate the diagrams involving instantaneous photon exchange both in the case of fermion self-energy as well as the vertex correction. We also show that the correspondence between the covariant and light front diagrams cannot be established if one removes the $k^{+}=0$ modes by an infrared cutoff before performing $k^{-}$ integration.

• Received 25 March 2005

DOI:https://doi.org/10.1103/PhysRevD.71.125011