The geometry and entanglement entropy of surfaces in loop quantum gravity

Understand

In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator.

• We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature and mean curvature.
• By investigating their properties, we shed light on the nature of the geometry of surfaces in loop quantum gravity.
• We also investigate the entanglement entropy across surfaces in the case where spin network edges are running within the surface.