expansion (1.19), the interaction terms in the QCD Lagrangian (1.40), as well as the quark, gluon and ghost propagators. In practice, this can be done via Wick’s theorem or using the Feynman rules for QCD, which can be derived from the QCD Lagrangian (1.40). Higher order terms in the expansion can be represented by Feynman diagrams that contain loops. For instance, consider the correlation function 〈 Ω | T [ Q ( x ) ¯ Q ( y ) ] | Ω 〉 , which is related to the amplitude for a quark to propagate between the spacetime points y and x in the presence of interactions. We will consider the next-to-leading order term in the perturbative expansion of this correlation function, which is O ( g $^{2}$). This is called the quark self-energy and can be represented by the Feynman diagram shown in Fig. 1.5. It is conventional to depict Feynman diagrams in momentum space, with the four-momentum of each propagator uniquely labeled. For brevity we will refer to four-momenta as momenta in what follows. The quark self-energy is represented by the Feynman diagram in Fig. 1.5 and is propor- tional to an integral over the momentum of the gluon. Schematically, the quark self-energy is given by Momentum integrals such as this are called loop integrals, because they emerge naturally from Feynman diagrams that contain loops. It should be understood that we are integrating over the entire infinite range of each integration variable, that is, the integration in (1.41) is over the entire volume of the four-dimensional momentum space. In what follows we will suppress the limits of integration in loop integrals. For brevity we have also omitted the iη 23 Σ ( q ) ≃ g 2 ∫ d $^{4}$k (2 π ) 4 1 k $^{2}$[ ( k + q ) 2 − m 2 ] . (1.41) Figure 1.5: Feynman diagram representing the quark self-energy. The quark propa- gates between the spacetime points y and x , and has momentum q at these locations. The quark interacts with a gluon that has momentum k , which flows from right to left in the diagram. Momentum is conserved at each vertex in the diagram.