从局部参考系的比较得到的宏观观测量
Macroscopic observables from the comparison of local reference systems
摘要：
由规范场规定的平行传输确定了局部参考系的集合。比较局部参考系在重叠区域导致一个合奏代数的关系运动学观测的规范理论，包括广义相对论。使用辅助细胞分解，我们提出了一个离散化的规范场的基础上的抽取所提到的运动学观测量的合奏。结果是表征测量尺度的“宏观可观测量”局部子代数的离散系综。这些宏观可观测量的一组估计被称为扩展格点规范场，因为它确定了$M$（以及继承胞腔分解的$M$的子流形）上的$G$ -丛以及嵌入格点上的格点规范场。在我们的宏观观测量代数中构造了一个物理观测量。正则化和粗粒化方面的初步研究，这是特殊的组合基地的规范场的描述，提出。在量子引力的背景下讨论了这种普通格点规范场的扩展的物理相关性。
英文摘要：
Parallel transport as dictated by a gauge field determines a collection of local reference systems. Comparing local reference systems in overlapping regions leads to an ensemble of algebras of relational kinematical observables for gauge theories including general relativity. Using an auxiliary cellular decomposition, we propose a discretization of the gauge field based on a decimation of the mentioned ensemble of kinematical observables. The outcome is a discrete ensemble of local subalgebras of ``macroscopic observables'' characterizing a measuring scale. A set of evaluations of those macroscopic observables is called an extended lattice gauge field because it determines a $G$-bundle over $M$ (and over submanifolds of $M$ that inherit a cellular decomposition) together with a lattice gauge field over an embedded lattice. A physical observable in our algebra of macroscopic observables is constructed. An initial study of aspects of regularization and coarse graining, which are special to this description of gauge fields over a combinatorial base, is presented. The physical relevance of this extension of ordinary lattice gauge fields is discussed in the context of quantum gravity.
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