Understanding Gauge

TL;DR

This paper clarifies the concept of gauge theories by distinguishing between formulations with excess structure, like electromagnetism, and those without, such as Yang-Mills theory and general relativity, providing a precise analysis of their structural differences.

Contribution

It offers a precise distinction between two usages of gauge theories and analyzes the presence of excess structure in different formulations, clarifying conceptual foundations.

Findings

Electromagnetism has excess structure in certain formulations.

Yang-Mills theory and general relativity generally lack excess structure.

The paper provides a formal criterion to distinguish these cases.

Abstract

I consider two usages of the expression "gauge theory". On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in which one formulation of electromagnetism, the paradigmatic gauge theory on both usages, may be understood to have excess structure, and then argue that gauge theories on the second usage, including Yang-Mills theory and general relativity, do not generally have excess structure in this sense.