New Aspect of Probabilistic Approach to Chern-Simons Theory

陈-西蒙斯理论概率方法的新观点

• 批准号: 20540120
• 负责人: MITOMA Itaru
• 金额: $ 2.83万
• 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: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540120/
• 关键词: Chern-Simonns 理論; 抽象ウィナー空間; ホロノミー; 漸近展開; スーパー・フィールド; 量子不変量; 超対称的場の量子論; 集合値確率積分; ファインマン積分; チャーン・サイモンズ汎関数; 集合値確率微分方程式; Chern-Simons積分; ウィナー空間; ファインマン測度; ウィナー測度; 位相不変量

To give a mathematical meaning to the Chern-Simons functional integral of its total Lagrangian in an abstract Wiener space setting, we regularize the 3rd terms including the infinite determinant appeared in the Lagrangian modified by the method of super fields, along the suggestions of my research colleague, Prof. Albeverio atthe University of Bonn in Germany and Prof. Funakubo in my University, and give themathematical definition as a Wiener functional. We did the estimate of the remainder terms in the asymptotic expansion by modifying the It^o method of defining the Feynman measure by using the Wiener measure. Concerning the Gauge theory including the Chern-Simons theory, we study the random surfaces from a viw point of set-valued stochastic processes. After defining the set-valued stochastic integral, we get the existence and uniqueness for the solutions of a set-valued stochastin differential equation undersome restriction. Metaphorically speaking the restriction in a word, we catch the motion of a jellyfish but not of an ameba.

To give a mathematical meaning to the Chern-Simons functional integral of its total Lagrangian in an abstract Wiener space setting, we regularize the 3rd terms including the infinite determinant appeared in the Lagrangian modified by the method of super fields, along the suggestions of my research colleague, Prof. Albeverio atthe University of Bonn in Germany and Prof. Funakubo in my University, and give themathematical definition as a Wiener功能。我们通过使用Wiener量度来定义Feynman度量的IT方法来对渐近扩展中其余项进行估计。关于包括Chern-Simons理论在内的量规理论，我们从设定值随机过程的VIW点研究了随机表面。在定义了设置值的随机积分后，我们获得了设置值stochastin微分方程的解决方案的存在和唯一性。隐喻地说，在单词中的限制时，我们抓住了水母的动作，而不是阿米巴的动作。

项目成果

On set-valued stochastic integrals in an M-type 2 Banach space

关于 M 型 2 Banach 空间中的集值随机积分

• DOI: 10.1016/j.jmaa.2008.09.017
• 发表时间: 2009-02
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: Shoumei Li;Itaru Mitoma;Yoshiaki Okazaki;Jinping Zhang
• 通讯作者: Jinping Zhang

Chern-Simons perturbation theory via Wiener space setting

通过维纳空间设定的 Chern-Simons 微扰理论

• 发表时间: 2009
• 作者: 種市信裕;関谷祐里;三苫至
• 通讯作者: 三苫至

Siegel modular forms of degree 2 over rings

环上 2 次西格尔模形式

• 发表时间: 2009
• 期刊: J.Number Theory 129
• 作者: S.Boecherer;Y.Hironaka;F.Sato;Takashi Ichikawa
• 通讯作者: Takashi Ichikawa

SET-VALUED STOCHASTIC DIFFERENTIAL EQUATION IN M-TYPE 2 BANACH SPACE

• DOI: 10.31390/cosa.4.2.06
• 发表时间: 2010-06
• 作者: I. Mitoma;Y. Okazaki;Jinping Zhang

Asymptotic expansion of perturbative Chern-Simons theory via Wiener space

微扰陈-西蒙斯理论通过维纳空间的渐近展开

• 发表时间: 2009
• 期刊: Bull. Sci. Math. 133
• 作者: Sergio Albeverio;Itaru Mitoma
• 通讯作者: Itaru Mitoma