5 Chapter 1: Introduction Although the terminology came later in [33], Nambu and Han [34] proposed a solution to the latter problem: quarks come not only in different flavors but also different colors. Phenomenologically one could posit that nature requires color neutrality to explain the former. In the same paper Nambu and Han in- troduced gauge vector fields associated with the quark color charge. Feynman rederived one of the previously mentioned scaling relations after developing the parton theory of nucleons: at high q 2 nucleons look like they are made up of point-like objects [35–38]. To agree with data nucleons have to be made up of not just the three valence quarks, but also sea quarks [39] and gluons [40]. While no experiment has yet to directly observe a bare quark or gluon (nor do we expect them to) there is strong indirect evidence for quarks from two jet events [41] and gluons from three [42] and four [43, 44] jet events; see Fig. 1.1. To describe the strong force binding quarks in nuclei, then, one wants a quantum field theory that becomes weaker at short distances. The idea of a non-Abelian gauge theory was introduced by Yang and Mills [45]; quantization was achieved by Faddeev and Popov [46], and ’t Hooft proved their renormaliz- ability [47]. After asymptotic freedom was first shown for non-Abelian theories [48, 49], it was proved that in four dimensions this property is unique to non- Abelian theories [50]. The infrared divergences of non-Abelian theories led to a natural explanation of confinement [51, 52], the inability to directly observe quarks or gluons. Experimental evidence for QCD as the theory of strong interactions is legion. At high momenta, for which perturbative methods are applicable, log