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  Non-commutative flux representation for loop quantum gravity

Baratin, A., Dittrich, B., Oriti, D., & Tambornino, J. (2011). Non-commutative flux representation for loop quantum gravity. Classical and quantum gravity, 28(17): 175011. doi:10.1088/0264-9381/28/17/175011.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-03F3-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-03F4-3
Genre: Journal Article

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1004.3450 (Preprint), 307KB
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 Creators:
Baratin, Aristide1, Author              
Dittrich, Bianca2, Author              
Oriti, Daniele3, Author              
Tambornino, Johannes1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              
2Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:102878              
3Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:67201              

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. Here we introduce a dual description of this space, by means of a Fourier transform mapping the usual loop gravity states to non-commutative functions on Lie algebras. We show that the Fourier transform defines a unitary equivalence of representations for loop quantum gravity. In the dual representation, flux operators act by star-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.

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 Dates: 2010-04-202011
 Publication Status: Published in print
 Pages: 21 pages, 1 figure
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 Rev. Method: -
 Identifiers: arXiv: 1004.3450
DOI: 10.1088/0264-9381/28/17/175011
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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: 28 (17) Sequence Number: 175011 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925513480_1