A curvature operator for LQG

Abstract

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.

20 pages; Labels on figure 4 and figure 5 adjusted and some references corrected

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