Dynamics for a 2-vertex Quantum Gravity Model

Understand

We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges.

• Such graphs represent two regions, in and out, separated by a boundary surface.
• We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective.
• In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity.