Renormalization and Renormalization Group: From the Discovery of UV Divergences to the Concept of Effective Field Theories

Abstract

Right from the beginning perturbative calculations in Quantum Field Theory have been plagued with infinities. Eventually, as a consequence of essential experimental input, and theoretical advances, a procedure, called renormalization, was discovered which generate finite answers, and allowed increasingly accurate calculations of Quantum Electrodynamics processes. The concept of renormalizable quantum field theories proved so successful that it could be applied to all fundamental interactions, but gravity: The Standard Model of Weak, Electromagnetic and Strong Interactions has now survived about 25 years of confrontation with experiments. Still the renormalization procedure itself remained an embarrassment for some theorists. A convergent set of ideas, coming both from particle physics and condensed matter, which can be grouped under the general name of renormalization group, finally suggested that renormalizable field theories should be understood as low energy effective field theories. We briefly review here the chain of ideas which led to this new and more consistent picture.