发表机构
Aix-Marseille Univ, Université de Toulon, CNRS, CPT; Sapienza University of Rome; ENEA, C.R. Frascati (Rome)（艾克斯-马赛大学、土伦大学、法国国家科学研究中心; 罗马第一大学; 意大利国家新能源与可再生能源署，弗拉斯卡蒂研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在量子层面实现规范固定条件，构造相应量子算符，证明均匀自旋网络态满足约束，从而在完整SU(2)对称的宇宙学理论与标准圈量子宇宙学之间建立联系。
AI 中文摘要
在这项工作中，我们在量子层面实现了规范固定条件，这些条件将描述经典宇宙学扇区的Ashtekar变量的均匀SU(2)规范理论与通常的迷你超空间表述联系起来。我们施加所谓的散度约束，该约束将规范固定为均匀规范，并在经典层面恢复一个有限维相空间，同时施加对角约束，该约束要求度量的对角性，并且已在文献中被广泛研究。我们为一般宇宙学模型构造了相应的量子算符，并提供了基于环量和通量的适当正则化。然后，我们利用在约化量子圈引力中发展的技术，证明了一类特殊的均匀自旋网络态，描述Bianchi I和Bianchi IX模型，满足量子规范固定约束。这通过所选态的有效阿贝尔结构，在具有完整SU(2)规范对称性的宇宙学理论与标准圈量子宇宙学之间建立了量子层面的联系。
英文摘要
In this work, we implement at the quantum level the gauge-fixing conditions that relate the homogeneous SU(2) gauge theory of Ashtekar variables, describing the classical cosmological sector, to the usual minisuperspace formulation. We impose the so-called divergence constraint, which fixes the gauge to the homogeneous one and, at the classical level, recovers a finite-dimensional phase space, together with the diagonal constraint, which imposes the diagonality of the metric and has already been extensively studied in the literature. We construct the corresponding quantum operators for general cosmological models and provide a suitable regularization in terms of holonomies and fluxes. We then show that a special class of homogeneous spin-network states describing the Bianchi I and Bianchi IX models satisfies the quantum gauge-fixing constraints, using techniques developed in Reduced Quantum Loop Gravity. This provides a quantum-level link between the cosmological theory with full SU(2) gauge symmetry and standard Loop Quantum Cosmology, by reason of the effective Abelian structure of the selected states.
Comments18 pages
