标题： 在保真结构在迷你超空间约简和LQC中的量子涨落中的作用 显示英文标题

标题： On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC

摘要： 在非紧致的时空极小超空间模型中，哈密顿量和辛形式中的空间积分必须通过将其限制到有限体积$V_o$来进行正则化，这个体积被称为参考单元。 由于在均一化约化之前的完整理论中这种限制是不必要的，参考单元的物理意义一直存在大量争论，特别是在环量子宇宙学的背景下。 理解其作用反过来对于评估极小超空间描述的有效性及其与全理论的联系是至关重要的。 在这项工作中，我们提出了一种在规范框架内将系统约化到空间均一和各向同性极小超空间的系统方法，并将其应用于一个质量标量场理论和引力。 我们的策略是通过在空间切片划分为可数多个不相交单元的离散场模式上引入第二类约束来实现空间均一性。 然后，约化理论的规范结构由相应的狄拉克括号给出。 重要的是，后者只能在拼接在一起的有限数量的单元上定义。 这确定了一个有限区域，即参考单元，其物理尺寸在经典层面上就具有明确的意义，作为施加均一性的尺度。 此外，该过程允许跟踪约化过程中丢失的信息以及误差如何依赖于$V_o$。 然后我们转向经典约化理论的量子化，重点研究不同$V_o$的理论之间的关系，并研究对统计矩、量子涨落和半经典态的影响。 在量子标量场的情况下，识别出全量子场理论的一个子领域，在其中可以再现“先约化后量子化”方法的结果，并且也确定了这种情况成为良好近似的条件。 显示英文摘要

摘要： In spatially non-compact minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume $V_o$, known as the fiducial cell. As this restriction is unnecessary in the complete theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of loop quantum cosmology. Understanding its role is in turn essential for assessing the minisuperspace description's validity and its connection to the full theory. In this work we present a systematic procedure for reduction to spatially homogeneous and isotropic minisuperspaces within the canonical framework and apply it to a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory's canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogenenity is imposed. Additionally, the procedure allows to track the information lost during reduction and how the error depends on $V_o$. We then move to the quantisation of the classically reduced theories, focusing on the relation between theories for different $V_o$, and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the "first reduced, then quantised" approach can be reproduced is identified and the conditions for this to be a good approximation are also determined.