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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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1004.3450 (Preprint), 307KB
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 Urheber:
Baratin, Aristide1, Autor           
Dittrich, Bianca2, Autor           
Oriti, Daniele3, Autor           
Tambornino, Johannes1, Autor           
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              
2Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              
3Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Schlagwörter: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Zusammenfassung: 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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 Datum: 2010-04-202011
 Publikationsstatus: Erschienen
 Seiten: 21 pages, 1 figure
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 Identifikatoren: arXiv: 1004.3450
DOI: 10.1088/0264-9381/28/17/175011
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Titel: Classical and quantum gravity
Genre der Quelle: Zeitschrift
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Ort, Verlag, Ausgabe: Bristol, U.K. : Institute of Physics
Seiten: - Band / Heft: 28 (17) Artikelnummer: 175011 Start- / Endseite: - Identifikator: ISSN: 0264-9381
CoNE: https://pure.mpg.de/cone/journals/resource/954925513480_1