Mathematics

Renormalization Group provides an unified framework for the rigorous understanding of apparently unrelated phenomena ranging from anomalies in Quantum Field Theory to universality in condensed matter or statistical physics. Universality or non-renormalization properties follow from a combination of the regularity properties of correlations, obtained establishing the convergence of the renormalized expansions, with Ward Identities, either exact or emerging. In the lectures we provide an overview of main results and an introduction to some key result, in particular to the vanishing of beta function and the existence of a line of fixed points.