On a partially reduced phase space quantisation of general relativity conformally coupled to a scalar field

TL;DR

This paper extends loop quantum gravity methods to include matter fields and a cosmological constant, providing detailed derivations and discussing the role of observables in a reduced phase space framework.

Contribution

It offers a detailed extension of previous work on loop quantum gravity to matter-coupled scenarios and explores the role of observables and deparametrisation in the quantisation process.

Findings

Extended loop quantum gravity to include matter and cosmological constant

Provided detailed derivations and calculations for the extended model

Discussed the role of observables and symmetry exchange in the quantisation

Abstract

The purpose of this paper is twofold: On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on 'loop quantum gravity without the Hamiltonian constraint' with calculational details and extend the results to standard model matter, a cosmological constant, and non-compact spatial slices. On the other hand, we provide a discussion on the role of observables, focussed on the situation of a symmetry exchange, which is key to our derivation. Furthermore, we comment on the relation of our model to reduced phase space quantisations based on deparametrisation.