The method of effective Lagrangian flow provides the most physically illuminating discussion of renormalisation theory. At distance scales much larger than some physical cutoff, the physics is described by a small number of parameters, which can be identified purely by dimensional analysis. For scalar theories a rigorous yet simple proof of renormalisability, based on this concept, was given by Polchinski, and this work forms the bedrock of this thesis.
For gauge theories there is the extra issue of the unitarity of the renormalised S-matrix, which can only be guaranteed by proving renormalised Ward identities, and this is what we carry out for all cases of interest in d = 4. In particular we cover the case of N = 1 super Yang-Mills.
We prove that the cancellation of anomalies at the one-loop level is a sufficient as well as necessary condition for a theory to be perturbatively quantisable, and hence that there are no higher-loop anomalies.
