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A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity


Cattaneo, Alberto Sergio; Perez, Alejandro (2017). A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity. Classical and Quantum Gravity, 34(10):107001.

Abstract

We show that the non-Abelian nature of geometric fluxes - the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG) - follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.

Abstract

We show that the non-Abelian nature of geometric fluxes - the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG) - follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:17 April 2017
Deposited On:18 Jan 2018 09:30
Last Modified:15 Mar 2018 20:47
Publisher:IOP Publishing
ISSN:0264-9381
OA Status:Closed
Publisher DOI:https://doi.org/10.1088/1361-6382/aa69b4

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