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

阿尔巴西奥和他的同事通过出现在Hida白噪声分析中的分布研究了Chern-Simons积分。站在积分的无穷级渐近中，我们可以用Wiener积分来改变Feynman积分，作者利用抽象维纳空间上的变分公式定义了威尔逊线的Chern-Simons积分，并讨论了如何在无限水平上消除积分的三次项，最后将其推广到微扰的Chern-Simons积分的Wiener空间方法中，并于1998年夏天在德国波恩大学举行的Dirichiet形式研讨会上作了特邀演讲。此外，还从Chern-Simons积分与三维流形的拓扑不变量之间的关系出发，对积分的局部化问题进行了严格的数学讨论。为了改变基本的维纳度量，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.