From Feynman diagrams to the amplituhedron: a gentle review

TL;DR

This paper reviews the computation of tree-level scattering amplitudes in Yang-Mills theory, illustrating the connection between traditional Feynman diagram calculations and the modern amplituhedron approach for a mathematical audience.

Contribution

It provides a detailed comparison between Feynman diagram methods and the amplituhedron framework for six-particle NMHV amplitudes, bridging physics and mathematics understanding.

Findings

Explicit derivation of six-particle NMHV amplitudes from Feynman diagrams

Demonstration of the amplituhedron's canonical form matching traditional formulas

Clarification of the geometric interpretation of scattering amplitudes

Abstract

In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail, in order to bridge the gap in understanding of the subject between mathematicians and physicists. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the $n=6, k=1, m=4$ amplituhedron.