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

Journal Article · Mon Aug 15 00:00:00 EDT 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4960823· OSTI ID:22596482

Stottmeister, Alexander; Thiemann, Thomas ^[1]

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1. Institut für Quantengravitation, Lehrstuhl für Theoretische Physik III, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7/B2, D-91058 Erlangen (Germany)

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.

• OSTI ID: 22596482
• Journal Information: Journal of Mathematical Physics, Vol. 57, Issue 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
BORN-OPPENHEIMER APPROXIMATION
EIGENSTATES
LIE GROUPS
LOOP QUANTUM GRAVITY
PERTURBATION THEORY
PHASE SPACE
QUANTIZATION