QCD recursion relations from the largest time equation

TL;DR

This paper derives BCFW recursion relations for gluons using the largest time equation in a specific gauge, providing a new perspective and potential generalizations to massive particles.

Contribution

It explicitly connects the BCFW recursion relations to the largest time equation, offering a novel proof and extension framework for gauge theories.

Findings

Derived BCFW recursion relations from the largest time equation

Established a connection between momentum space identities and the largest time equation

Extended the approach to include massive scalars and fermions

Abstract

We show how by reassembling the tree level gluon Feynman diagrams in a convenient gauge, space-cone, we can explicitly derive the BCFW recursion relations. Moreover, the proof of the gluon recursion relations hinges on an identity in momentum space which we show to be nothing but the Fourier transform of the largest time equation. Our approach lends itself to natural generalizations to include massive scalars and even fermions.