发表机构
Gdańsk University of Technology; University of Wrocław（格但斯克理工大学; 弗罗茨瓦夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对圈量子宇宙学中聚合物量子化产生不可分离希尔伯特空间的问题，以平坦各向同性宇宙为例检验积分希尔伯特空间方法的动力学，发现其长期半经典性质与单 sector 方法无显著差异，并对比了旧数值方法与 Eigen 库的应用效果。
AI 中文摘要
应用于圈量子引力/宇宙学的聚合物量子化程序会产生不可分离的希尔伯特空间。通常，人们通过挑选并在可分离的超选 sector 中工作来回避该问题，但在超出各向同性的更复杂模型中，这种方法往往不再适用。在另一种方法中，人们将可分离的希尔伯特空间构建为所有可用 sector 的积分。本文以允许负宇宙学常数和无质量标量场的平坦各向同性宇宙为例，对后一种方法导出的动力学进行检验。对初始半经典态的数值演化表明，与单 sector 方法相比，其长期半经典性质无显著差异。此外，本文还将旧的（针对特定问题的）数值方法与更通用、更高效的标准工具（Eigen 库）的应用进行了比较。
英文摘要
Polymer quantization program applied in Loop Quantum Gravity/Cosmology leads to nonseparable Hilbert spaces. Commonly, one sidesteps this problem by singling out and working with a separable superselection sector. This is however often no longer accessible in more involved models beyond isotropic ones. In an alternative approach one builds a separable Hilbert space as an integral over all available sectors. Here we test the dynamics following from the latter on the example of a flat isotropic Universe admitting negative cosmological constant and a massless scalar field. There, numerical evolution of (initially) semiclassical states shows that there is no relevant difference in their long term semiclassicality properties in comparison to those in a single sector approach. Further, the older (problem-specific) numerical methods are compared against an application of more common and more efficient standard tools (eigen library).
Comments24 pages, 12 figures, 2 listings, accepted by Physical Review D
