微扰BF理论
Perturbative BF theory
摘要：
本文考虑拓扑型超重标化规范理论，其中结构群等于非齐次群ISU（2）。导出了规范场的关联函数的生成泛函，并讨论了它与Chern-Simons理论生成泛函的关系。给出了R^3中定义的这个模型的完全重归一化。确定了ISU（2）共轭类的结构。规范不变观测量是通过与定向、框架和着色结相关联的ISU（2）完整性的适当归一化迹来定义的。威尔逊线的期望值的微扰评估的调查和高达三阶的贡献，对应于结不变量的观测量的微扰扩展，产生。得出了纽结观测量对框架的一般依赖关系。
英文摘要：
We consider a superrenomalizable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its connection with the generating functional of the Chern-Simons theory is discussed. The complete renomalization of this model defined in R^3 is presented. The structure of the ISU(2) conjugacy classes is determined. Gauge invariant observables are defined by means of appropriately normalized traces of ISU(2) holonomies associated with oriented, framed and coloured knots. The perturbative evaluation of the Wilson lines expectation values is investigated and the up-to-third-order contributions to the perturbative expansion of the observables, which correspond to knot invariants, are produced. The general dependence of the knot observables on the framing is worked out.
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