Chapter 1 Introduction 1.1 Introduction Overview The advance of physics in the last few centuries has been relentless. One of the main themes of this advance has been the desire for unification, the ultimate aim being to have one theory that describes all the fundamental forces. A major step towards this goal was achieved in the nineteenth cen- tury, when separate descriptions of electricity and magnetism were unified into a single theory of electromagnetism. It wasn’t until the 1930s that it was fully appreciated that electromagnetism was an example of a gauge theory. A gauge theory, in its most general sense, is a model with an invariance under a local symmetry of some of the variables in the theory [4,5]. In the case of QED, the phases on all the fields can be changed locally, and so long as we introduce a gauge field which connects the points of local relabelling, the physics remains unchanged. In QED, for example, the quanta of these gauge fields are called photons. 2