Abel Chern-Simons理论、Stokes定理和广义联络
Abelian Chern-Simons theory, Stokes' theorem, and generalized connections
摘要：
广义联系及其演算是在量子引力的背景下发展起来的。在这里，我们将其应用到阿贝尔陈-西蒙斯理论。本文利用Stokes定理、通量算子和广义联络导出了U（1）Chern-Simons理论中完整性的期望值。一个框架的holonomy循环出现在我们的建设，我们展示了如何，通过选择自然的框架，由此产生的期望值，但定义一个功能超过规范不变的圆柱函数。本文中考虑的阿贝尔理论是我们的方法的测试用例。它也可以应用于非阿贝尔理论。该病例的结果将在其他地方报告。
英文摘要：
Generalized connections and their calculus have been developed in the context of quantum gravity. Here we apply them to abelian Chern-Simons theory. We derive the expectation values of holonomies in U(1) Chern-Simons theory using Stokes' theorem, flux operators and generalized connections. A framing of the holonomy loops arises in our construction, and we show how, by choosing natural framings, the resulting expectation values nevertheless define a functional over gauge invariant cylindrical functions. The abelian theory considered in the present article is test case for our method. It can also be applied to the non-abelian theory. Results for that case will be reported elsewhere.
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