The Semi-Classical Limit of Quantum Gravity on Corners

TL;DR

This paper explores the connection between quantum and classical descriptions of corner symmetries in quantum gravity, using Berezin quantization and coherent states to relate quantum observables to classical geometric quantities like area.

Contribution

It introduces a novel framework linking representation-theoretic quantum observables to classical geometric variables in quantum gravity, especially for spacetimes with horizons.

Findings

Established a method to relate quantum corner symmetry observables to classical geometry.

Applied the formalism to static, spherically symmetric spacetimes with horizons.

Demonstrated the utility of Berezin quantization in quantum gravity contexts.

Abstract

We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes \mathrm{H}_3,$ which arises in the context of quantum gravity. We relate quantum observables -- specified by representation-theoretic data -- to their classical counterparts using generalized Perelomov coherent states and the framework of Berezin quantization. This procedure links abstract representation-theoretic input to geometric classical observables, such as area. We conclude by applying the formalism to static, spherically symmetric spacetimes admitting a horizon.