Equivalence of One Loop Diagrams in Covariant and Light Front QED Revisited

TL;DR

This paper revisits and generalizes the proof of equivalence between covariant and light-front QED at the one-loop level, emphasizing the necessity of the third term in the photon propagator for the equivalence to hold.

Contribution

It extends previous work by proving the equivalence for all components of the vertex correction diagram in light-front QED, highlighting the importance of the third photon propagator term.

Findings

Equivalence holds only with the third photon propagator term.

Generalized proof for all vertex correction components.

Reinforces the necessity of specific gauge terms in light-front QED.

Abstract

We revisit the proof of equivalence of one loop expressions for fermion self-energy and vertex correction in light-front QED and Covariant QED at the Feynman diagram level and generalize, to all components, the proof of equivalence for the one loop vertex correction diagram which was presented earlier by us only for the $+$ component of $\Lambda^\mu$. We demonstrate, in the general case also, that the equivalence cannot be established without the third term in the three-term photon propagator in light cone gauge.