Project/Area Number  09640279 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  SAGA UNIVERSITY 
Principal Investigator 
MITOMA Itaru Saga University, Faculty of Science and Engneering, Professor, 理工学部, 教授 (40112289)

CoInvestigator(Kenkyūbuntansha) 
INOUE Atsushi Tokyo Institute of Technology, Graduate School of Science and Engineering, Profe, 大学院理工学研究科, 教授 (40011613)
河合 茂生 佐賀大学, 文化教育学部, 教授 (30186043)
NISHI Akio Saga University, Faculty of Culture and Education, Professor, 文化教育学部, 教授 (60022274)
KUBO Masahiro Saga University, Faculty of Science and Engneering, Associate Professor, 理工学部, 助教授 (80205129)
ICHIKAWA Takashi Saga University, Faculty of Science and Engneering, Professor, 理工学部, 教授 (20201923)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Chern Simons integral / super fields / method of stationary phase / Wiener spsce / Ink invariant / topological invariant / ChernSimons積分 / スーパーフィールド / 停留位相法 / ウィナー空間 / リンク不変量 / 位相不変量 / 確率解析 / chernSimons積分 / リーマン面 
Research Abstract 
Albeverio and his colleague have studied the ChernSimons 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 ChernSimons 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 in Wiener space approach to a perturbative Chern  Simons integral and 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 ChernSimons integral and the topological invariants of 3manifold. 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.
