Abelian 2+1D Loop Quantum Gravity Coupled to a Scalar Field

TL;DR

This paper develops an exact quantization of a simplified abelian 3D loop quantum gravity model coupled to a scalar field, addressing key issues like inverse metric definition and representation choices.

Contribution

It introduces a novel exact quantization method for the U(1)^3 model, providing insights into quantum gravity-matter coupling and foundational problems.

Findings

Exact quantization of the U(1)^3 model achieved

Addresses inverse metric and representation issues in quantum gravity

Provides a framework applicable to 4D quantum gravity problems

Abstract

In order to study 3d loop quantum gravity coupled to matter, we consider a simplified model of abelian quantum gravity, the so-called U(1)^3 model. Abelian gravity coupled to a scalar field shares a lot of commonalities with parameterized field theories. We use this to develop an exact quantization of the model. This is used to discuss solutions to various problems that plague even the 4d theory, namely the definition of an inverse metric and the role of the choice of representation for the holonomy-flux algebra.