Equivalence of Covariant and Light Front QED: Generating Instantaneous Diagrams

TL;DR

This paper demonstrates that instantaneous photon exchange diagrams and infrared singularities in light front QED can be derived from covariant expressions by taking an asymptotic limit, simplifying calculations.

Contribution

It shows that using the two-term photon propagator and asymptotic limits reproduces instantaneous diagrams and IR singularities from covariant QED expressions.

Findings

Instantaneous photon exchange diagrams can be generated from covariant expressions.

IR singularities in propagating diagrams are reproduced via asymptotic limits.

Method simplifies the derivation of light front QED diagrams from covariant forms.

Abstract

One loop expressions for fermion self energy,vacuum polarization and vertex correction in light front time ordered perturbation theory (LFTPOT) can be obtained from respective covariant expressions by performing k^- integration. In earlier work, we have shown that the third term in the doubly transverse gauge propagator is necessary to generate the diagrams involving instantaneous photon exchange both in case of fermion self-energy as well as vertex correction.In this work,we show that instantaneous photon exchange diagrams in fermion self-energy as well as th IR singular terms in the propagating diagrams can be generated by taking the asymptotic limit of the covariant expression,if one uses the commonly used two term photon propagator.We also show that this method reproduces the IR singular terms in propagating diagrams of vacuum polarization.