Why surplus structure is not superfluous

TL;DR

This paper uses category theory to clarify the role of surplus gauge structure, showing it is essential for representing local, physically relevant fields in gauge theories.

Contribution

It provides a precise categorical analysis demonstrating the necessity of surplus structure in theories with local, physically meaningful gauge fields.

Findings

Surplus structure is essential for representing local gauge fields.

Category-theoretic tools clarify the role of surplus structure.

Surplus structure is not superfluous but functionally necessary.

Abstract

The idea that gauge theory has 'surplus' structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this paper, we employ category-theoretic tools to illuminate an aspect of this puzzle. We precisify what is meant by 'surplus' structure by means of functorial comparisons with equivalence classes of gauge fields, and then show that such structure is essential for any theory that represents a rich collection of physically relevant fields which are 'local' in nature.