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

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.

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

References in corpus (3)

• From twistors to twisted geometries
• U(N) tools for Loop Quantum Gravity: The Return of the Spinor
• Dynamics for a 2-vertex Quantum Gravity Model

Cited by in corpus (4)

• Just Renormalizable TGFT's on U(1)^d with Gauge Invariance
• Dynamics for a 2-vertex Quantum Gravity Model
• Deformation Operators of Spin Networks and Coarse-Graining
• Spinors and Twistors in Loop Gravity and Spin Foams