标题： 量子约化圈引力：关于运动学和动力学的新视角 显示英文标题

标题： Quantum-reduced loop gravity: New perspectives on the kinematics and dynamics

摘要： 我们提出了一种系统的方法来研究量子约化圈量子引力的运动学，这是一个由Alesci和Cianfrani最初提出的模型，旨在探索圈量子引力的物理意义。 我们通过在圈量子引力的运动学Hilbert空间上引入一个主约束算符，实现了量子约化圈量子引力背后的量子规范固定程序，该算符表示一组经典上约束密度三角形为对角线的规范条件。 量子约化圈量子引力的标准Hilbert空间可以作为主约束算符解的空间恢复，而另一方面，主约束方法为考虑标准构造的可能推广提供了一个有用的起点。 我们还研究了量子约化框架下单个六价节点态的量子动力学。 我们发现，控制这些态的动力学的哈密顿量在形式上与圈量子宇宙学中的Bianchi I模型的哈密顿约束有密切的相似性。 显示英文摘要

摘要： We present a systematic approach to the kinematics of quantum-reduced loop gravity, a model originally proposed by Alesci and Cianfrani as an attempt to probe the physical implications of loop quantum gravity. We implement the quantum gauge-fixing procedure underlying quantum-reduced loop gravity by introducing a master constraint operator on the kinematical Hilbert space of loop quantum gravity, representing a set of gauge conditions which classically constrain the densitized triad to be diagonal. The standard Hilbert space of quantum-reduced loop gravity can be recovered as a space of solutions of the master constraint operator, while on the other hand the master constraint approach provides a useful starting point for considering possible generalizations of the standard construction. We also examine the quantum dynamics of states consisting of a single six-valent node in the quantum-reduced framework. We find that the Hamiltonian which governs the dynamics of such states bears a close formal resemblance to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology.