Description

Scattering amplitudes give the probabilities for different outcomes of any particle scattering experiment, for example at the Large Hadron Collider in CERN. They are notoriously diffficult to compute however, so that even many of the scattering amplitudes relevant for analysing results at the LHC and in particular distinguishing new physics from known physics are not known.

Feynman diagrams are a basic method for calculating scattering amplitudes of particles in quantum field theory. However, to compute even quite a simple amplitude can involve summing many thousands of diagrams. However the final expressions can be remarkably simple, resulting from delicate and unexpected cancellations between terms and implying that there should be a better way to compute them.

A few years ago, just such a new method was discovered that radically simplifies the computation and replaces the method of Feynman diagrams by a recursion relation. Surprisingly this relies on little more than some general physical principles and Cauchy's theorem in complex analysis, and should have been discovered decades ago.

The project would begin by discussing the basic features of quantum field theory applied to perturbative QCD (the theory of the strong nuclear force) and possibly also quantum gravity. It would then derive the recursion relations. There might be scope to apply the relations to compute new processes.

Prerequisites

Resources

One will first need a basic familiairity with quantum field theory, in particular Feynman diagrams and gauge theory. Introductory texts on quantum field theory such as  Quantum Field Theory in a Nutshell by A.Zee, Princeton University Press, Quantum Field Theory by Itzykson, C. and Zuber, J. B. New York: McGraw-Hill, 1980 or Quantum Field Theory of Point Particles by Brian Hatfield will be useful.
However we will hopefully not need too much in order to understand the basics of the original paper describing the new method:
by Britto, Cachazo,Feng and Witten "Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory"