# Scalar curvature operator for models of loop quantum gravity on a cubical graph

@inproceedings{Lewandowski2021ScalarCO, title={Scalar curvature operator for models of loop quantum gravity on a cubical graph}, author={Jerzy Lewandowski and Ilkka Makinen}, year={2021} }

In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator is defined on the Hilbert space of a fixed cubical graph. The starting point of our work is to write the spatial Ricci scalar classically as a function of the densitized triad. We pass from the classical expression to a quantum operator through a…

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