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

References in corpus (8)

• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Gravity quantized
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Rainbow metric from quantum gravity
• Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups
• Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
• Chiral symmetry breaking and theta vacuum structure in QCD

Cited by in corpus (8)

• Backreaction in Cosmology
• Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups
• Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
• Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology
• Surface state decoherence in loop quantum gravity, a first toy model
• Strict deformation quantization of abelian lattice gauge fields
• Classical, semiclassical and quantum signatures of quantum phase transitions in a (pseudo) relativistic many-body system
• Loop quantum gravity with optimal control path integral, and application to black hole tunneling