The Lagrangian origin of MHV rules

TL;DR

This work derives the MHV (CSW) rules directly from pure Yang–Mills theory by constructing a canonical transformation on light-front quantisation surfaces. The transformation maps the standard light-front YM action, with $L_2$, $L^{++-}$, $L^{--+}$, and $L^{--++}$, to an action $S_L$ whose Feynman rules are MHV vertices connected by scalar propagators, effectively encoding the off-shell continuation in the spinor structure on the quantisation surface. Analyticity arguments and the prescription $p\to p-\mu\,p^2/(2p\cdot\mu)$ ensure the off-shell vertices reproduce on-shell MHV amplitudes, while the construction extends to massless quarks via a fermionic canonical transformation that preserves the measure. This framework opens a path toward systematic loop computations within a four-dimensional, light-front formalism, subject to regulator and zero-mode considerations.

Abstract

We construct a canonical transformation that takes the usual Yang-Mills action into one whose Feynman diagram expansion generates the MHV rules. The off-shell continuation appears as a natural consequence of using light-front quantisation surfaces. The construction extends to include massless fermions.