标题： 霍夫斯和阿什特卡-列文斯基测度 显示英文标题

标题： Hyphs and the Ashtekar-Lewandowski Measure

摘要： 在Ashtekar框架中广义连接的空间$\Ab$的性质被研究。首先给出了一种构造新连接的方法。新的平行变换仅在经过固定路径初始段的路径上与原始变换不同。这与一种新的路径独立性概念密切相关。尽管我们不限制于浸入的光滑或解析情况，但任何有限路径集都依赖于一个有限的独立路径集，即所谓的hyph。这分别推广了已知的光滑网络集和解析图集的定向性。由于这些命题，一方面，从$\Ab$到格点规范理论的投影是满射且开的。另一方面，可以为每个紧致结构群定义一个诱导的Haar测度，而不管路径所使用的光滑性类别如何。 显示英文摘要

摘要： Properties of the space $\Ab$ of generalized connections in the Ashtekar framework are investigated. First a construction method for new connections is given. The new parallel transports differ from the original ones only along paths that pass an initial segment of a fixed path. This is closely related to a new notion of path independence. Although we do not restrict ourselves to the immersive smooth or analytical case, any finite set of paths depends on a finite set of independent paths, a so-called hyph. This generalizes the well-known directedness of the set of smooth webs and that of analytical graphs, respectively. Due to these propositions, on the one hand, the projections from $\Ab$ to the lattice gauge theory are surjective and open. On the other hand, an induced Haar measure can be defined for every compact structure group irrespective of the used smoothness category for the paths.