A curvature operator for LQG
  We introduce a new operator in Loop Quantum Gravity - the 3D curvature operator - related to the 3-dimensional scalar curvature. The construction is based on Regge Calculus. We define it starting from the classical expression of the Regge curvature, then we derive its properties and discuss some explicit checks of the semi-classical limit. 
Emanuele Alesci, Mehdi Assanioussi, Jerzy Lewandowski
gr-qc hep-th