Calculation of $\beta$ functions with FeynCalc

One important calculation in any Quantum Field Theory is the determination of the beta functions of the theory. The final result can be summarized in very simple terms, but the student needs to have done it at least once to understand it fully. The procedure for QED is very easy and can be looked up in many texts, like my own on-line course, Advanced Quantum Field Theory.

For more complicated cases, like a non-abelian gauge theory, the calculation is much more involved. That is here that the symbolic calculations using FeynCalc can be useful. To show how things can be setup, I have made a detailed calculation for QED and scalar QED using the conventions of my text. Relevant information can be obtained in the following files:

• The mathematica input file, BetaQED.m, for FeynCalc in QED.
• The mathematica input file, BetaScalarQED.m, for FeynCalc in Scalar QED.