THE CONFORMAL GROUP AND APPLICATIONS TO HIGH ENERGY PHYSICS

Abstract

Conformal symmetry is respected by several physical systems. In High Energy Physics, it can be used to study non-perturbative QCD via the AdS/CFT correspondence. This thesis focuses on the partial wave expansions of conformal fourpoint functions that are traditionally described as functions of cross ratios. We describe these functions group theoretically and find that they are characterised by H-bi-invariant spherical functions. A connection to traditional cross ratios is then only a change a variables from the parameters of the maximal abelian subgroup of the conformal group. In the Minkowski setting, causality plays a central role and is described group theoretically by semigroups. The representation theory of these semigroups imposes non-trivial restrictions on the fourpoint functions and the conformal partial wave expansions. In this thesis, we establish these claims and provide a framework constructing these conformal partial waves in an embedding space approach. We conclude with a discussion on open problems.