| Project/Area Number |
25610015
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tohoku University (2014-2015)
Keio University (2013) |
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Principal Investigator |
MAEDA YOSHIAKI 東北大学, 知の創出センター, 特任教授(研究) (40101076)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 変形量子化 / 超弦理論 / ケーラー多様体 / 非可換ゲージ理論 / 量子場理論 / 素粒子物理学 / 国際交流ベルギー / 厳密変形量子化 / 量子幾何学 / ループ空間の幾何学 / 無限次元シンプレクティック幾何学 / 無限次元空間の特性類 / シンプレクティック作用 / 国際研究者交流アメリカ / 国際情報交流アメリカ / 幾何学 / ループ空間 / 無限次元リー群 / アメリカ / ベルギー / フランス |
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| Outline of Final Research Achievements |
This study is a challenge for constructing a field theory from a non-commutative geometrical point of view. The original idea for this study is to use the deformation quantization, in particular, our advantage is to use the non-formal deformation quantization. By using this, we construct the non-commutative gauge theory on 4-manifolds. Other topic we have worked is to study infinite dimensional categories of deformation quantization via psued differential operators. In particular, we construct characteristic classes for loop space by using the regularization method. As an application, we showed the non-triviality of the fundamental group of the group of diffeomorphisms of 5 dimensional compact manifolds.
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