Feynman rules for QED, QCD and the SM

We give here, without derivation, the rules for calculating (up to a sign) what is known as the Feynman amplitude M in QED, QCD and the SM. We illustrate with a few topical examples. A detailed treatment can be found in Bjorken and Drell (1965) and in Cutler and Sivers (1978). 

The rules for calculating the Feynman amplitude M are essentially universal and irrespective of the normalization convention for the states. 

Clearly, however, the matrix elements (/ 5 i) of the 5-operator depend upon the normalization convention, so the relationship between (/151i) and M will be convention dependent. 

Often it is useful to use other normalization conventions. To read off the analogue of (A2.1.2) it is simplest to avoid the complications of continuum normalization and Dirac 6-function by quantizing the system in a finite volume V. The key connection is the equivalence 

If we prefer to utilize states normalized to unity in the volume V, i.e. 

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