标题： 在最小超空间约简和LQC中参考结构的作用 显示英文标题

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

摘要： 我们研究在规范框架下标量场理论和引力的齐次迷你超空间约化。 通过第二类约束对非紧致空间片$\Sigma$的分区中的场模进行对称性约化。 通过相关的狄拉克括号获得结果齐次理论的规范结构，该括号只能在有限数量的均匀拼接的单元上定义，并与全理论的泊松括号在平均场中一致。 这确定了一个有限区域$V_o$，即参考单元，其大小$L$确定了施加齐性的物理尺度，即波长截断。 约化理论的结果来自 1) 选择全理论中$V_o$平均可观测量的一个子集；2) 忽略波长为$\lambda\geq L$和$\lambda< L$的非均匀$\vec k\neq\mathbf0$模式；3) 忽略编码相邻单元之间相互作用的边界项。 误差的阶数为$\mathcal O(1/kL)$。 因此，约化理论的非壳结构依赖于$V_o$的大小，不同的$V_o$识别出规范不等价的理论，尽管它们的动力学是$V_o$-无关的。 它们的量子化然后导致一个由$V_o$标记的量子表示族，而对$V_o$的主动缩放的量子版本通过不同理论之间的适当保持动力学的同构来实现。 我们讨论在标准和聚合量子化中对统计矩、涨落和半经典态的后果。 对于质量为$m$的标量场，我们还简要描述了量子约化，并确定了QFT的一个子领域，在该领域中，只要$m\gg1/L$，就可以很好地近似再现"先约化后量子化"理论的结果。最后，概述了一种在宇宙学中包含非均匀性的策略。 显示英文摘要

摘要： We study the homogeneous minisuperspace reduction within the canonical framework for a scalar field theory and gravity. Symmetry reduction is implemented via second class constraints for the field modes over a partitioning of the non-compact spatial slice $\Sigma$ into disjoint cells. The canonical structure of the resulting homogeneous theories is obtained via the associated Dirac bracket which can only be defined on a finite number of cells homogeneously patched together and agrees with the full theory Poisson bracket for the averaged fields. This identifies a finite region $V_o$, the fiducial cell, whose size $L$ sets the physical scale over which homogeneity is imposed, namely a wavelength cutoff. The reduced theory results from 1) selecting a subset of $V_o$-averaged observables of the full theory; 2) neglecting inhomogeneous $\vec k\neq\mathbf0$ modes with wavelengths $\lambda\geq L$ and $\lambda< L$; 3) neglecting boundary terms encoding interactions between neighbouring cells. The error made is of order $\mathcal O(1/kL)$. As a result, the off-shell structures of the reduced theory depend on the size of $V_o$ and different $V_o$ identify canonically inequivalent theories whose dynamics though is $V_o$-independent. Their quantisation leads then to a family of $V_o$-labeled quantum representations and the quantum version of an active rescaling of $V_o$ is implemented via a suitable dynamics-preserving isomorphism between the different theories. We discuss the consequences for statistical moments, fluctuations, and semiclassical states in both a standard and polymer quantisation. For a scalar field of mass $m$, we also sketch the quantum reduction and identify a subsector of the QFT where the results of the"first reduced, then quantised" theories can be reproduced with good approximation as long as $m\gg1/L$. Finally, a strategy to include inhomogeneities in cosmology is outlined.