Past and future of gauge theory

Abstract

A brief account is sketched on how the doctrine based on local gauge invariance developed over the years, turning into a pivotal element in model building for elementary particles. This principle owes its success to being renormalizable order by order in the perturbation expansion for small coupling strengths. An important point is the requirement of unitarity and locality, which shows up in the details of the Feynman rules. After gauge fixing, one finds that the system displays an elegant new symmetry: BRST invariance. Recent experimental findings in the Large Hadron Collider may point the way to the future. To capture new clues for the future, we must bear in mind the fundamental successes of steps that were made in the past.