Symbolic Algebra and Renormalization of Gauge Theories

Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of gauge theories. This scheme is readily implemented using the general purpose package, Mathematica. The techniques discussed are used to calculate renormalization group functions for a non-abelian $SU(m)$ gauge theory with massless fermions in a representation R, in the two-loop approximation, and to simplify some expressions arising in electroweak calculations at the two loop level.