Review of the CHY Formalism - Master Thesis

Abstract

The Cachazo-He-Yuan (CHY) formalism describes interactions among sub-atomic particles and allows the computation of scattering amplitudes. It is equivalent to, and at the same time fundamentally different from, the perturbative treatment of quantum field theory using Feynman diagrams (up to tree-level). It deals in particular with the scattering of n massless particles in an arbitrary D-dimensional flat space-time. This is achieved by a map from momentum space to the Riemann sphere with punctures. Starting from this map, we discuss the so-called Scattering Equations, the proof for their polynomial form by Dolan and Goddard, and their general solution in terms of the determinant of a (n−3)!×(n−3)! matrix. A program in Mathematica to perform these involved calculations for general n is given as well. Finally, we briefly discuss of how the scattering amplitudes can be obtained.