Infinite-Dimensional Stochastic approach to Geometrical Objects

我们(Mitoma-Nishikawa)在抽象的Wiener空间中给出了Chern-Simons积分关于Wilson线的摄动单圈逼近的数学定义，并证明了渐近展开定理。在此基础上，计算了三维曲面的系数，得到了链式不变量。结果现已准备好提交。本文利用Wiener空间给出了摄动Chern-Simons积分的有限部分的数学定义和无穷部分的渐近估计。这一结果发表在波恩大学的SFB，611上。

We,(Mitoma-Nishikawa),gave a mathematical definition for perturbative 1-loop approximation of the Chern-Simons integral with respect to the Wilson lines in an abstract Wiener space setting and proved the asymptotic expansion theorem. Further we calculate the copefficients for 3-dimensional surface and obtained link invariants. The result is now prepared for submission. We,(Albeverio-Mitoma),gave mathematical definitions for finite part and asymptotic estimate for infinite part of perturbative Chern-Simons integral via Wiener space. The result is appeared in SFB,611 in Bonn University.