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  Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity

Giesel, K., & Thiemann, T. (2010). Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity. Classical and quantum gravity, 27(17): 175009. doi:10.1088/0264-9381/27/17/175009.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5FE6-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-4868-7
Genre: Journal Article

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 Creators:
Giesel, Kristina1, Author
Thiemann, Thomas1, Author              
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: We perform a canonical, reduced phase space quantisation of General Relativity by Loop Quantum Gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of 1. the Brown -- Kuchar mechanism in the presence of pressure free dust fields which allows to deparametrise the theory and 2. Rovelli's relational formalism in the extended version developed by Dittrich to construct the algebra of gauge invariant observables. Since the resulting algebra of observables is very simple, one can quantise it using the methods of LQG. Basically, the kinematical Hilbert space of non reduced LQG now becomes a physical Hilbert space and the kinematical results of LQG such as discreteness of spectra of geometrical operators now have physical meaning. The constraints have disappeared, however, the dynamics of the observables is driven by a physical Hamiltonian which is related to the Hamiltonian of the standard model (without dust) and which we quantise in this paper.

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 Dates: 2010
 Publication Status: Published in print
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 Identifiers: eDoc: 321636
arXiv: 0711.0119v1
DOI: 10.1088/0264-9381/27/17/175009
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Title: Classical and quantum gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 27 (17) Sequence Number: 175009 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1