Background-Independence from the Perspective of Gauge Theory

TL;DR

This paper analyzes background independence and diffeomorphism invariance in general relativity, contrasting them with gauge theories, and clarifies their roles and distinctions in the formulation of gravitational theories.

Contribution

It identifies when gauge theories become background independent and extends this understanding to gravity, clarifying misconceptions about active diffeomorphism invariance.

Findings

Gauge theories become background independent at specific formulation stages

General relativity's background independence is clarified and distinguished from gauge invariance

Active diffeomorphism invariance is not unique to general relativity

Abstract

We consider two concepts often discussed as significant features of general relativity (particularly when contrasted with the other forces of the Standard Model): background independence and diffeomorphism invariance. We remind the reader of the role of backgrounds both as calculational tools and as part of the formulation of theories. Examining familiar gauge theory constructions, we are able to pinpoint when in the formulation of these theories they become background independent. We then discuss extending the gauge formulation to gravity. In doing so we are able to identify what makes general relativity a background independent theory. We also discuss/dispel suggestions that "active" diffeomorphism invariance is a feature unique to general relativity and we go on to argue against the claim that this symmetry is the origin of background independence of the theory.