U(N) invariant dynamics for a simplified Loop Quantum Gravity model
General Relativity and Quantum Cosmology
2015-05-20 v1
Abstract
The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.
Cite
@article{arxiv.1012.3832,
title = {U(N) invariant dynamics for a simplified Loop Quantum Gravity model},
author = {Enrique F. Borja and Jacobo Díaz-Polo and Iñaki Garay and Etera R. Livine},
journal= {arXiv preprint arXiv:1012.3832},
year = {2015}
}
Comments
4 pages, to appear in Proceedings of Spanish Relativity Meeting 2010 (ERE 2010) held in Granada, Spain