Equivalence of covariant and light front QED at one loop level

Abstract

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 ${k}^{\ensuremath{-}}$ 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 ${k}^{\ensuremath{-}}$ integration.