QCD recursion relations from the largest time equation

TL;DR

The paper derives the BCFW recursion relations for tree-level gluon amplitudes by reexpressing space-cone gauge-fixed Yang-Mills diagrams, showing that a momentum-space identity is the Fourier transform of the largest time equation. It provides a field-theoretic proof that amplitudes factorize into products of lower on-shell amplitudes with shifted, on-shell momenta, and demonstrates this explicitly for several points, including the crucial 5-point case. The authors connect the recursion to the causality structure of quantum field theory through the largest time equation and extend the framework to include massive scalars and fermions. The work suggests potential loop-level applications and generalizations, offering a principled basis for on-shell methods in QCD and related theories.

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.

Figures (2)

• Figure 1: Factorization of the 4-point function
• Figure 2: Factorization of the 5-point function