2014 Fiscal Year Final Research Report
Noncommutative functional identites with non formal deformation quantization and its application
| Project/Area Number |
24540097
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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 |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
OMORI Hideki 東京理科大学, 理工学部, 教授 (20087018)
MAEDA Yoshiaki 東北大学, 理学部, 教授 (40101076)
MIYAZAKI Naoya 慶應義塾大学, 経済学部, 教授 (50315826)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 変形量子化 / シンプレクティック幾何学 / ポアソン幾何学 / 非可換幾何学 / 量子化 / 力学 |
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| Outline of Final Research Achievements |
We consider non-formal deformation quantizaztion. In the obtained star product aligebra, we consider star exponntaials. Using the star exponentials, we can construct certain noncommutative functional identites. As an application, we investigate a concrete MIC-Kepler problem, its eigenvalues, and also its noncommutative symplectic reduction, with non formal star products. Based on the investitation on the MIC-Kepler problem,we extend the noncommutative reduction to general situation with S1 symmetry group.
Using star exponentials,we also obtain vacumms, with which we can obtain
representation of non-formal star product algebras.
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| Free Research Field |
シンプレクティック・ポアソン幾何学、変形量子化
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