An Introduction to Gauge Theories

Abstract

All lectures on gauge theories start with a discussion of the reasons why these theories have been the subject of so much interest in the last seven or eight years. On the one hand, these justifications are less and less necessary as time goes on; on the other, the reasons are changing. To respect to this tradition, I shall list briefly a few of the recent achievements of gauge theories: The success of quantum electrodynamics (QED), the first gauge theory (or the second, if one wants to consider Einstein’s theory of gravitation as a particular gauge theory). The unification of weak and electromagnetic interactions, using Yang-Mills fields (1), and the various predictions which came out of it, particularly the existence of neutral currents. The proof of the renormalizability of massive gauge theories (abelian and non abelian). The predictions of massless gauge theory of strong interactions (chromodynamics), particularly asymptotic freedom and, perhaps, confinement. The possibility to unify strong interactions with the others (weak and electromagnetic). The development of supersymetric theories, and recent progresses in the theory of super-gravity.