在由圈量子引力启发的有效模型中检验广义协变性
Testing general covariance in effective models motivated by Loop Quantum Gravity
AI总结：
本文提出一种检验有效量子引力理论广义协变性的判据，将其应用于圈量子引力中带逆三元组与和乐修正的球对称真空模型，发现除哈密顿量修正外还需对经典度规进行量子修正才能保证广义协变性。
摘要：
在这项工作中，我们引入了一个用于检验有效量子引力理论中广义协变性的判据。它将爱因斯坦-希尔伯特作用量在一般时空微分同胚下的不变性分析适配到有效正则模型的情形。虽然主要目的是检验在圈量子引力中得到的模型，但该判据并不限于那些物理系统，也可应用于任何以正则形式表述的修正引力理论。因此，这里的方法不是寻找一个有效模型，而是考察一个由量子修正哈密顿量所表示的给定模型。具体而言，我们将该判据应用于真空中的球对称时空，其中包含作为圈量子化程序结果而出现的逆三元组和和乐修正。研究发现，除了对哈密顿量的初始修正之外，还需要对经典度规本身进行量子修正，才能得到广义协变的模型。讨论中还包括了与近期替代判据的比较。
英文摘要：
In this work we introduce a criterion for testing general covariance in effective quantum gravity theories. It adapts the analysis of invariance under general spacetime diffeomorphisms of the Einstein-Hilbert action to the case of effective canonical models. While the main purpose is to test models obtained in Loop Quantum Gravity, the criterion is not limited to those physical systems and may be applied to any canonically formulated modified theory of gravity. The approach here is hence not that of finding an effective model, but rather to examine a given one represented by a quantum corrected Hamiltonian. Specifically, we will apply the criterion to spherically symmetric spacetimes in vacuum with inverse triad and holonomy modifications that arise as a consequence of the loop quantization procedure. It is found that, in addition to the initial modifications of the Hamiltonian, quantum corrections of the classical metric itself are needed as well in order to obtain generally covariant models. A comparison with recent alternative criteria is included in the discussion.
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