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

Chern-Simons积分、超场和固定相方法的研究

• 批准号: 09640279
• 负责人: MITOMA Itaru
• 金额: $ 1.92万
• 依托单位: SAGA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640279/
• 关键词: Chern Simons integral; super fields; method of stationary phase; Wiener spsce; Ink invariant; topological invariant; 確率解析; chern-Simons積分; リーマン面

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.

Albeverio 和他的同事通过 Hida 白噪声分析中出现的分布研究了 Chern-Simons 积分。另一方面，在积分的无限级渐近中，我们可以用维纳积分改变费曼积分，首席研究员通过抽象维纳空间上的变量变化公式定义了威尔逊线的陈-西蒙斯积分并讨论了如何消除无穷级积分的三次项，最后总结为微扰陈-西蒙斯积分的维纳空间方法，并在波恩大学举办的Dirichiet forms Workshop上受邀演讲1998年夏天在德国。进一步的问题是对有关Chern-Simons积分和3-流形拓扑不变量之间关系的积分定域性进行严格的数学讨论。为了改变基本的维纳测度，或者为了确保数学中的超域方法可能是不可避免的。

项目成果

久保雅弘(剣持氏と共著): "Weak solutions of non-linear systems for non-isothermal phase transitions" Advances in Mathematcal Scieuces and Applications. (掲載予定).

Masahiro Kubo（与 Kenmochi 先生合着）：“非等温相变非线性系统的弱解”数学科学与应用进展（即将出版）。

市川尚志: "Schottky uniformigation theory on Riemann surfaces and Munford curves of infinite genus" J.Reine Angew.Math.486. 45-68 (1997)

Takashi Ichikawa：“黎曼曲面和无限亏格的 Munford 曲线上的肖特基均匀化理论”J.Reine Angew.Math.486 (1997)。

三苫至: "One loop approximation of the Charn-Simoxs integral" Volume in hoxor of 70th birthday of T.Hida, World Seientific. (掲載予定).

Itaru Mitoma：“Charn-Simoxs 积分的单循环近似”卷，T.Hida 70 岁生日，World Seientific（即将出版）。

Takashi Ichikawa: "Schottky uniformization theory on Riemann surfaces and Munford curves of infinite genus" J.Reine Angew.Math.486. 45-68 (1997)

Takashi Ichikawa：“黎曼曲面和无限亏格的 Munford 曲线上的肖特基均匀化理论”J.Reine Angew.Math.486。