The amplituhedron

Description

Scattering amplitudes give the probabilities for different outcomes of any particle scattering experiment, for example at the Large Hadron Collider in CERN and are in some sense the fundamental quantities of theoretical particle physics. Feynman diagrams are the traditional method for calculating scattering amplitudes of particles in quantum field theory you will learn in AQT4. However, to compute even quite a simple amplitude can involve summing many thousands of diagrams. In the last few years it has been discovered that ( at least in one quantum field theory) the amplitudes have a completely novel and remarkable alternative description as the volume of certain polyhedra and their generalisations (in fact generalising in the simplest case volumes of polygons).

In this project we will examine this dual description of amplitudes. One can either probe this in a more mathematical direction, (understanding the polyhedra in question and its generalisations and how to obtain rational expressions from them, without worrying too much about the physics origin) or a more physicsy direction (focussing on the physics origin and only touching on the ampltiuhedron interpretation.

Prerequisites

Resources

A popular description can be found here quanta magazine article
Wikepedia gives a more technical summary https://en.wikipedia.org/wiki/Amplituhedron
You can google for other popular descriptions. Apart from that the best place to look is the original paper https://arxiv.org/pdf/1312.2007.pdf