Scalar curvature operator for quantum-reduced loop gravity

TL;DR

This paper extends a scalar curvature operator to quantum-reduced loop gravity, deriving its explicit form and analyzing its expectation values on basis states, advancing the understanding of geometric operators in simplified quantum gravity models.

Contribution

It introduces and explicitly formulates a scalar curvature operator within quantum-reduced loop gravity, a simplified model of quantum gravity.

Findings

Explicit form of the curvature operator derived

Expectation values computed for basis states

Provides a practical example of operator application

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.