English

Dynamics for a simple graph using the U(N) framework for loop quantum gravity

General Relativity and Quantum Cosmology 2015-05-30 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 find an interesting global U(N) symmetry in this model that selects the homogeneous/isotropic sector. Then, we propose a quantum Hamiltonian operator for this reduced sector. Finally, we introduce the spinor representation for LQG in order to propose a classical effective dynamics for this model.

Keywords

Cite

@article{arxiv.1110.6017,
  title  = {Dynamics for a simple graph using the U(N) framework for loop quantum gravity},
  author = {Enrique F. Borja and Jacobo Diaz-Polo and Laurent Freidel and Iñaki Garay and Etera R. Livine},
  journal= {arXiv preprint arXiv:1110.6017},
  year   = {2015}
}

Comments

4 pages. Proceedings of Loops'11, Madrid. To appear in Journal of Physics: Conference Series (JPCS)

R2 v1 2026-06-21T19:26:45.208Z