Deformation quantizations for instantons and related noncommutative deformations of topological invariants
| Project/Area Number |
23540117
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science (2013-2015)
Kushiro National College of Technology (2011-2012) |
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Principal Investigator |
Sako Akifumi 東京理科大学, 理学部, 准教授 (00424200)
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| Co-Investigator(Kenkyū-buntansha) |
MAEDA Yoshiaki 東北大学, 知の創出センター, 教授 (40101076)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
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)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 非可換幾何 / 変形量子化 / ゲージ理論 / BPS方程式 / インスタントン / ケーラー多様体 / 局所対称空間 / 微分幾何 / モノポール / 国際研究者交流 / イタリア / ポーランド / ベルギー / イギリス / ドイツ |
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| Outline of Final Research Achievements |
Gauge theories on noncommutative homogeneous Kahler manifolds have been studied. To make the noncommutative manifolds, we used the deformation quantization with separation of variables for Kahler manifolds which was given by Karabegov. We constructed models of noncommutative gauge theories that are connected with usual Yang-Mills theories in the commutative limits. As examples, we gave noncommutative CP^N and noncommutative CH^N at first and construct gauge theories on them. In order to make theories as non-formal power series, the Fock representations of the noncommutative manifolds were constructed, too. Using the representations, the Euler-Lagrange equations and the BPS equations (including an instanton type equation) of the gauge theories were derived, and nontrivial solutions were also obtained.
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Report
(6 results)
Research Products
(30 results)
