Diffeomorphism invariance in spherically symmetric loop quantum gravity

TL;DR

This paper examines how diffeomorphism invariance is recovered in a loop quantum gravity model of Schwarzschild space-time, highlighting limitations due to holonomic variables that mirror expectations in the full theory.

Contribution

It demonstrates the partial recovery of diffeomorphism invariance in a loop quantum gravity approach and discusses the implications of using holonomic variables.

Findings

Diffeomorphism invariance is recovered with limitations.

Loop quantization aligns with metric variable quantization in the physical Hilbert space.

Limitations resemble behaviors expected in the full loop quantum gravity theory.

Abstract

We study the issue of the recovery of diffeomorphism invariance in the recently introduced loop quantum gravity treatment of the exterior Schwarzschild space-time. Although the loop quantization agrees with the quantization in terms of metric variables in identifying the physical Hilbert space, we show that diffeomorphism invariance in space-time is recovered with certain limitations due to the use of holonomic variables in the loop treatment of the model. This resembles behaviors that are expected in the full theory.