Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity
General Relativity and Quantum Cosmology
2016-08-01 v1
Abstract
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.
Cite
@article{arxiv.1503.05943,
title = {Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity},
author = {Seramika Ariwahjoedi and Jusak Sali Kosasih and Carlo Rovelli and Freddy P. Zen},
journal= {arXiv preprint arXiv:1503.05943},
year = {2016}
}
Comments
16 pages, 10 figures