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  On the role of the Barbero-Immirzi parameter in discrete quantum gravity

Dittrich, B., & Ryan, J. P. (2013). On the role of the Barbero-Immirzi parameter in discrete quantum gravity. Classical and quantum gravity, 30(9): 095015.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-EB27-2 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-16A1-1
Genre: Journal Article

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 Creators:
Dittrich, Bianca1, Author              
Ryan, James P.1, Author              
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
 Abstract: The 1-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them Loop Quantum Gravity and Spin Foams. It facilitates the loop quantization programme and subsequently the Barbero-Immirzi parameter (gamma) arises in both the spectra of geometrical operators and in the dynamics provided by Spin Foams. However, the debate continues as to whether quantum physics should be Barbero-Immirzi parameter dependent. Starting from a discrete SO(4)-BF theory phase space, we find two possible reductions with respect to a discrete form of the simplicity constraints. The first reduces to a phase space with gamma-dependent symplectic structure and more generally in agreement with the phase space underlying Loop Quantum Gravity restricted to a single graph - a.k.a. Twisted Geometries. The second, fuller reduction leads to a gamma-independent symplectic structure on the phase space of piecewise-flat-linear geometries - a.k.a. Regge geometries. Thus, the gamma-dependence of physical predictions is related to the choice of phase space underlying the quantization.

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 Dates: 2012-09-212013
 Publication Status: Published in print
 Pages: 16 + 12 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1209.4892
eDoc: 10.1088/0264-9381/30/9/095015
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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: 30 (9) Sequence Number: 095015 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1