Some surprising implications of background independence in canonical quantum gravity

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.

To appear in the special issue of General Relativity and Gravitation, dedicated to the memory of Professor Juergen Ehlers. 16 pages

References in corpus (3)

• Loop Quantum Cosmology: An Overview
• Semiclassical states for quantum cosmology
• Fundamentals of Quantum Gravity

Cited by in corpus (10)

• Loop Quantum Cosmology: A Status Report
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• Flux formulation of loop quantum gravity: Classical framework
• Loop quantum gravity coupled to a scalar field
• Unimodular Loop Quantum Cosmology
• Observations on interfacing loop quantum gravity with cosmology
• The classical limit of a state on the Weyl algebra
• The Koslowski- Sahlmann representation: Gauge and diffeomorphism invariance
• A new realization of quantum geometry
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR