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Article Dans Une Revue International Journal of Geometric Methods in Modern Physics Année : 2015

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

Résumé

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.

Dates et versions

hal-01258356 , version 1 (18-01-2016)

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Seramika Ariwahjoedi, Jusak Sali Kosasih, Carlo Rovelli, Freddy P. Zen. Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity. International Journal of Geometric Methods in Modern Physics, 2015, 12, pp.1550112. ⟨hal-01258356⟩
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