Diffeomorphism invariance and general covariance: a pedagogical introduction

TL;DR

This paper clarifies the concepts of diffeomorphism invariance and general covariance, emphasizing their importance in spacetime physics and correcting common misconceptions about their relationship and significance.

Contribution

It provides a pedagogical introduction that distinguishes between diffeomorphism invariance and general covariance, clarifying their roles in physics beyond General Relativity.

Findings

Diffeomorphism invariance is often misunderstood as exclusive to General Relativity.

The paper clarifies the distinction between diffeomorphism invariance and general covariance.

It emphasizes the broader significance of these concepts in spacetime physics.

Abstract

Diffeomorphism invariance is a feature that gets sometimes highlighted as something with profound implications in the physics of spacetime. Moreover, it is often wrongly associated exclusively with General Relativity. The fact that diffeomorphism invariance and general covariance are used interchangeably does not help. Here, we attempt at clarifying these concepts.