An exploration of gauge theory and spinors on a spacetime manifold

Abstract

In this thesis, we will explore the mathematical model behind the Standard Model. In the Standard Model, there are two types of particles: force carriers and matter particles. We will see that every force carrier can be modelled by a gauge field, whose structure is given by a Lie group, and spin-half matter particles by a spinor, whose structure depends on the double cover of a rotation group. We will consider these fields first on Minkowski space (special relativity) and later on a general spacetime manifold (general relativity), for which we need to introduce the basics of differential geometry. The focus of this thesis will be that of a specific force carrier and matter particle: the photon and the electron and their interaction.