Background independence and field redefinitions in quantum gravity

TL;DR

This paper demonstrates that in quantum gravity, background independence and diffeomorphism invariance, including field redefinitions, cannot be simultaneously maintained within a path-integral framework.

Contribution

It reveals a fundamental tension between background independence and diffeomorphism invariance in quantum gravity path integrals, highlighting a key conceptual challenge.

Findings

Background independence and diffeomorphism invariance are incompatible in path-integral approaches.

Field redefinitions as diffeomorphisms contribute to the tension.

The result impacts the formulation of consistent quantum gravity theories.

Abstract

It is generally believed that a full-fledged theory of quantum gravity should exhibit background independence and diffeomorphism invariance. In its most general form, the latter comprises field redefinitions, which are diffeomorphisms in configuration space. We show that any path-integral approach to quantum gravity leads to a tension between these properties, such that they cannot hold simultaneously.