A computable framework for Loop Quantum Gravity

TL;DR

This paper develops a non-perturbative, loop quantum gravity-based framework for quantizing general relativity with matter fields, using dust as a natural time variable to facilitate physical calculations.

Contribution

It introduces a novel non-perturbative quantization approach for gravity coupled with matter, utilizing dust as a time variable within the loop quantum gravity framework.

Findings

Constructed a physical Hilbert space for the model

Derived a physical Hamiltonian with spatial diffeomorphism symmetry

Established a framework for practical calculations in quantum gravity

Abstract

We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The methods of loop quantum gravity applied to this model lead to a physical Hilbert space and Hamiltonian. This provides a framework for physical calculations in the theory.