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arXiv · 1012.3832

U(N) invariant dynamics for a simplified Loop Quantum Gravity model

Enrique F. Borja·Jacobo Díaz-Polo·Iñaki Garay·Etera R. Livine
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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.

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Enrique F. Borja, Jacobo Díaz-Polo, Iñaki Garay, Etera R. Livine. 2010-12-17. U(N) invariant dynamics for a simplified Loop Quantum Gravity model. https://doi.org/10.1088/1742-6596%2F314%2F1%2F012041

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