Scalar curvature operator for quantum-reduced loop gravity

Abstract

In a previous article we have introduced an operator representing the three-dimensional scalar curvature in loop quantum gravity. In this article we examine the new curvature operator in the setting of quantum-reduced loop gravity. We derive the explicit form of the curvature operator as an operator on the Hilbert space of the quantum-reduced model. As a simple practical example, we study the expectation values of the operator with respect to basis states of the reduced Hilbert space.