The Problem Of Gauge Theory

TL;DR

This paper discusses the conceptual and mathematical foundations of quantizing gauge theories, explores approaches like perturbation and lattice methods, and highlights the significance of the mass gap in quantum gauge theory for understanding the universe.

Contribution

It provides a conceptual overview of quantizing gauge theories, connecting perturbation theory, lattice approximations, and the importance of the mass gap in four-dimensional quantum gauge theories.

Findings

Quantum gauge theory in four dimensions is believed to have a mass gap.

Lattice approximations can make gauge theory more concrete.

The mass gap is fundamental to the structure of the universe.

Abstract

I sketch what it is supposed to mean to quantize gauge theory, and how this can be made more concrete in perturbation theory and also by starting with a finite-dimensional lattice approximation. Based on real experiments and computer simulations, quantum gauge theory in four dimensions is believed to have a mass gap. This is one of the most fundamental facts that makes the Universe the way it is. This article is the written form of a lecture presented at the conference "Geometric Analysis: Past and Future" (Harvard University, August 27-September 1, 2008), in honor of the 60th birthday of S.-T. Yau.