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  On the space of generalized fluxes for loop quantum gravity

Dittrich, B., Guedes, C., & Oriti, D. (2013). On the space of generalized fluxes for loop quantum gravity. Classical and quantum gravity, 3(5): 055008. doi:10.1088/0264-9381/30/5/055008.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-E979-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-E97C-1
Genre: Journal Article

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1205.6166 (Preprint), 396KB
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 Creators:
Dittrich, Bianca1, Author              
Guedes, Carlos2, Author              
Oriti, Daniele2, Author              
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              
2Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: We show that the space of generalized fluxes - momentum space - for loop quantum gravity cannot be constructed by Fourier transforming the projective limit construction of the space of generalized connections - position space - due to the non-abelianess of the gauge group SU(2). From the abelianization of SU(2), U(1)^3, we learn that the space of generalized fluxes turns out to be an inductive limit, and we determine the consistency conditions the fluxes should satisfy under coarse-graining of the underlying graphs. We comment on the applications to loop quantum cosmology, in particular, how the characterization of the Bohr compactification of the real line as a projective limit opens the way for a similar analysis for LQC.

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 Dates: 2012-05-282013
 Publication Status: Published in print
 Pages: 25 pages, 2 figures
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1205.6166
DOI: 10.1088/0264-9381/30/5/055008
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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: 3 (5) Sequence Number: 055008 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1