Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity

We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2+1)-dimen...

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Bibliographic Details
Published inInternational journal of geometric methods in modern physics Vol. 12; no. 10
Main Authors Ariwahjoedi, Seramika, Kosasih, Jusak Sali, Rovelli, Carlo, Zen, Freddy
Format Journal Article
LanguageItalian
Published World Scientific Publishing 2015
Subjects
General Relativity and Quantum Cosmology
Physics
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ISSN0219-8878
DOI10.1142/S0219887815501121

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Summary:We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2+1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.
ISSN:0219-8878
DOI:10.1142/S0219887815501121