2006 Fiscal Year Final Research Report Summary
Infinite-Dimensional Stochastic approach to Geometrical Objects
| Project/Area Number |
17540124
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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, Mathematics, Professor, 理工学部, 教授 (40112289)
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| Co-Investigator(Kenkyū-buntansha) |
OGURA Yukio Saga University, Mathematics, Professor, 理工学部, 教授 (00037847)
TANIGUCHI Setsuo Kyushu University, Mathematics, Professor, 大学院・数理学研究院, 教授 (70155208)
ICHIKAWA Takashi Saga University, Mathematics, Professor, 理工学部, 教授 (20201923)
AIDA Shigeki Osaka University, Mathematics, Professor, 大学院・基礎工学研究科, 教授 (90222455)
HANDA Kenji Saga University, Mathematics, Associate Professor, 理工学部, 助教授 (10238214)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Chern-Simons integral / Wiener space / Wilson line / Holonomy / Topological invariant / Topological field theory / Superstring |
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| Research Abstract |
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.
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[Book] 確率論入門I2006
Author(s)
池田信行, 小倉幸雄, 高橋陽一郎, 眞鍋昭治郎
Total Pages
323+x
Publisher
培風館
Description
「研究成果報告書概要(和文)」より
