Some surprising implications of background independence in canonical quantum gravity

TL;DR

This paper explains how background independence uniquely determines the kinematic structure of loop quantum gravity, highlighting the powerful role of diffeomorphism invariance in non-perturbative quantum gravity.

Contribution

It provides a pedagogical explanation of why background independence leads to a unique kinematic algebra in LQG, emphasizing the significance of diffeomorphism invariance.

Findings

Background independence uniquely determines LQG kinematics.

Diffeomorphism invariance plays a crucial role in non-perturbative quantum gravity.

The paper clarifies the implications of background independence for quantum gravity approaches.

Abstract

There is a precise sense in which the requirement of background independence suffices to uniquely select the kinematics of loop quantum gravity (LQG). Specifically, the fundamental kinematic algebra of LQG admits a unique diffeomorphism invariant state. Although this result has been established rigorously, it comes as a surprise to researchers working with other approaches to quantum gravity. The goal of this article is to explain the underlying reasons in a pedagogical fashion using geometrodynamics, keeping the technicalities at their minimum. This discussion will bring out the surprisingly powerful role played by diffeomorphism invariance (and covariance) in non-perturbative, canonical quantum gravity.