标题： 全量子引力中的微分同胚不变宇宙对称性 显示英文标题

标题： Diffeomorphism invariant cosmological symmetry in full quantum gravity

摘要： 本文总结了一种新的提议，用于在微分同胚不变水平上严格定义环量子引力的一个领域，该领域对应于均匀和各向同性的宇宙学，从而能够详细比较环量子引力和环量子宇宙学的结果。 我们已完成的关键技术步骤是（a）在广义相对论的经典相空间上以微分同胚协变的方式表述均匀性和各向同性的条件，以及（b）使用已充分理解的技术一致地将这些条件转换到环量子引力中。 一些额外的步骤，例如构建环量子宇宙学的希尔伯特空间到全理论中的（分布）态空间的具体嵌入，尚未完成。 然而，我们还描述了作为一个概念验证，对均匀和各向同性环量子宇宙学嵌入到Ashtekar和Wilson-Ewing的量子Bianchi I模型的完整分析。 细节将在即将发表的两篇论文中出现。 显示英文摘要

摘要： This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.