QED is an example of an Abelian gauge theory: the order in which two gauge transformations, G $_{1}$, G $_{2}$, are performed is irrelevant. It is possible to construct gauge theories that are non-Abelian, meaning that the order in which two (or more) gauge transformations are performed does matter. In fact it was discovered in the 1970s that this was exactly what was needed to describe both the weak force and the strong force, which make up two more of the four fundamental forces. The force which we have yet to come to is gravity. Currently gravity is a bit of an enigma in the particle physics world: classically it is well described by the theory of general relativity [6, 7], and there are no experimental measurements which contradict its predictions. However it is hard to test gravity at a single particle level because it is so weak in comparison to the other three forces. However almost everyone be- lieves that general relativity needs modification; as it stands at the moment it cannot be quantized, which would make it unique amongst all the other forces. How to quantize gravity has been the bane of quantum physicists for generations, and there are currently two prongs of attack: loop quantum gravity [8], and string theory [9–11], on which we will spend some further time in section 1.4. However the theme of this thesis is QCD, so it is prudent to review some of the features of this non-Abelian gauge theory. In the late 1940s and early 1950s, only a few ‘elementary particles’ were known: the proton, neutron, electron, neutrino and photon. Almost the entire observable universe consists of just these particles. However, some puzzling unstable particles had been seen in cosmic rays. Furthermore, 3 1.2 QCD