U(N) invariant dynamics for a simplified loop quantum gravity model

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

In spite of the several approaches to implement the dynamics within the loop quantum gravity theory, this is still an open problem. In this talk we will discuss a tentative dynamics for the simplest class of graphs in loop quantum gravity: Two vertices linked with an arbitrary number of edges (this model represents two regions, in and out, separated by a boundary surface). We will use the recently introduced U(N) framework in order to identify area creation and annihilation operators. Then, we will propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface, and we will explore physical applications and possible generalizations of this model.