Spherically Symmetric Quantum Geometry: States and Basic Operators

TL;DR

This paper develops the quantum geometric framework for spherically symmetric models in loop quantum gravity, extending previous homogeneous models to inhomogeneous cases with field theory features.

Contribution

It introduces a detailed comparison between reduced quantization and derivation from the full theory for inhomogeneous spherically symmetric quantum geometry.

Findings

Extended the quantum geometric framework to inhomogeneous models.

Compared reduced quantization with full theory derivation.

Discussed implications for Einstein-Rosen waves.

Abstract

The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory aspects arise. A comparison between a reduced quantization and a derivation of the model from the full theory is presented in detail, with an emphasis on the resulting quantum representation. Similar concepts for Einstein-Rosen waves are discussed briefly.