Research of Chern-Simons Integral, Super Fields and Method of Stationary Phase

Albeverio和他的同事利用希达白色噪声分析中出现的分布研究了Chern-Simons积分。另一方面，在积分的无穷级渐近性中，我们可以用维纳积分来代替费曼积分，主要研究者在抽象Wiener空间上用变量变换公式定义了Wilson线的Chern-Simons积分，讨论了如何在无限水平上消除积分的三次项，最后总结了在Wiener空间上对微扰Chern-Simons积分的逼近。Simons积分于1998年夏天在德国波恩大学的Dirichiet形式研讨会上作了特邀演讲。进一步的问题是对涉及到Chern-Simons积分与三维流形拓扑不变量之间关系的积分局部化问题进行数学上的严格讨论。为了改变基本的维纳测度，或者为了确定数学中的超域方法，可能是不可避免的。

Albeverio and his colleague have studied the Chern-Simons integral by the distribution appeared in the Hida White Noise Analysis. Standing on the other point that in the infinite level asymptotics of the integral we may change the Feynman integral by the Wiener integral, the head investigator defines the Chern-Simons integral for the Wilson lines by the formula of change of variables on the abstract Wiener space and discuss how to eliminate the cubic term of the integral in the infinite level and finally summarize it inWiener space approach to a perturbative Chern - Simons integraland gave an invited speaking in the Workshop of Dirichiet forms held at Bonn University in Germany on the summer of 1998.Further problem is to give a mathematically rigorous discussion about the localization of the integral concerning with the relation between the Chern-Simons integral and the topological invariants of 3-manifold. For the purpose to change the basic Wiener measure may be needed or to make sure the method of super fields in mathematics may be inevitable.