Coherent states, quantum gravity and the Born-Oppenheimer approximation, III: Applications to loop quantum gravity

TL;DR

This paper explores how Weyl quantisation for compact Lie groups integrates with loop quantum gravity models, proposing it as a key tool for applying space adiabatic perturbation theory to overcome canonical quantisation challenges.

Contribution

It demonstrates the compatibility of Weyl quantisation with loop quantum gravity's phase space, enabling the use of space adiabatic perturbation theory in this context.

Findings

Weyl quantisation aligns with loop quantum gravity phase space.

Proposes Weyl quantisation as a tool for space adiabatic perturbation theory.

Facilitates overcoming Born-Oppenheimer approximation obstacles in quantum gravity.

Abstract

In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity.