标题： 量子简化的环引力中的标量曲率算子 显示英文标题

标题： Scalar curvature operator for quantum-reduced loop gravity

摘要： 在之前的一篇文章中，我们引入了一个表示圈量子引力中三维标量曲率的算子。 在本文中，我们在量子约化圈引力的框架下研究了这个新的曲率算子。 我们推导了该曲率算子在量子约化模型的希尔伯特空间上的显式形式。 作为一个简单的实际例子，我们研究了该算子相对于约化希尔伯特空间基态的期望值。 显示英文摘要

摘要： 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.