content_image/295906.jpg
Some of these terms are shown in Fig. 1.4. 

<img src='content_image/295906.jpg'>

Note that the Feynman diagrams in Fig. (1.4) are connected, that is, all of the propagators are linked to one another. However, the perturbative expansion of the numerator in Eq. (1.19) includes disconnected diagrams. Diagrams of this type represent vacuum processes. It can be shown that the denominator of Eq. (1.19) serves to cancel all disconnected diagrams that arise in the perturbative expansion. In practice this cancellation can be implemented by simply ignoring terms in the perturbative expansion that correspond to disconnected diagrams. 

Feynman diagrams can be used as mnemonics to keep track of terms in the perturba- tive expansion of a correlation function. Using Wick’s theorem and the expression for the perturbative expansion (1.19), it is possible to relate each diagram component to a certain mathematical expression. These are called Feynman rules. One of the Feynman rules for QCD is that every quark line in a Feynman diagram mathematically corresponds to a quark propagator (1.14). Another is that every quark-gluon vertex is associated with a factor of i g $_{2}$λ $^{a}$γ$^{µ}$. This vertex rule can be derived easily using Wick’s theorem and the perturbative expansion. The Feynman rules for QCD are given in Ref. [100]. Note, however, that any correlation function can be calculated using Wick’s theorem. It is important to emphasize that Wick’s theorem is more fundamental than the Feynman rules. 

