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.

v3: Typos corrected in Eqs. (4.58), (4.60) and (B.26) and in Table 1. Results presented in section 5 not affected (correct equations were used when performing the calculations). v2: Minor clarifications added. Version accepted for publication. v1: 31 pages, 4 figures

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Cited by in corpus (2)

• Master constraint approach to quantum-reduced loop gravity
• On the dynamics of single-vertex states in quantum-reduced loop gravity