| Project/Area Number |
09640279
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | SAGA UNIVERSITY |
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Principal Investigator |
MITOMA Itaru Saga University, Faculty of Science and Engneering, Professor, 理工学部, 教授 (40112289)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| 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)
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| Keywords | 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 |
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| Research Abstract |
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 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 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.
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