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arXiv · 2211.04826

Scalar curvature operator for quantum-reduced loop gravity

Jerzy Lewandowski·Ilkka Mäkinen
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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.

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Jerzy Lewandowski, Ilkka Mäkinen. 2022-11-09. Scalar curvature operator for quantum-reduced loop gravity. https://doi.org/10.1103/physrevd.107.126017

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