Deformation quantization and noncommutative geometry
| Project/Area Number |
15540094
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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 |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
YOSHIOKIA Akira Tokyo University of Science, Department of Mathematics Faculty of Science, Professor, 理学部, 教授 (40200935)
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| Co-Investigator(Kenkyū-buntansha) |
OMORI Hideki Tokyo University of Science, Department of Mathematics Faculty of Science and Technology, Professor, 理工学部, 教授 (20087018)
HARA Tamio Tokyo University of Science, Department of Mathematics Faculty of engineering, Professor, 工学部, 教授 (10120205)
MAEDA Yoshiaki Keio University, Department of mathematical science, Faculty of Science and Technology, Professor, 理工学部, 教授 (40101076)
MIYAZAKI Naoya Keio University, Department of Mathematics, Faculty of Economics, Assistant Professor, 経済学部, 助教授 (50315826)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2004: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2003: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Deformation quantization / Star product / Symplectic geometry / Quantization / Hamiltonian mechanics / Hamiltonian mechanics / gerbe / Lie group / Deformation Quantization / gerb / Deformation quantizalion / Hamiltonia mechanics |
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| Research Abstract |
By means of a complex symmetric matrix K, we have a linear isomorphism from the Weyl algebra to the space of all polynomial P(C,2n). We introduce a topology into the space P(C,2n) with respect to which the induced product is smooth, and we can take the completion. The star exponential belongs to the complete space. We investigate the two constructions of the star exponential function of the quadratic forms in P(C,2n). One is given by the path integral methods and the other is given by solving an ordinary differential equation. We investiageted the associated bundle structure over the space of symmetric matrices. We also investigate the noncommutative complex projective space given by convergent star products. In future we will study the extended concept of bundle structure which naturally enters through convergent star product algebras.
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Report
(3 results)
Research Products
(35 results)
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[Book] 量子的な微分積分2005
Author(s)
大森 英樹
Total Pages
376
Publisher
シュプリンガーフェアラーク東京
Description
「研究成果報告書概要(和文)」より
Related Report
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[Book] 数学のなかの物理学2004
Author(s)
大森 英樹
Total Pages
343
Publisher
東大出版会
Description
「研究成果報告書概要(和文)」より
Related Report
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[Book] 量子的な微分積分2004
Author(s)
大森 英樹, 前田 吉昭
Total Pages
337
Publisher
シュプリンガーフェアラーク東京
Related Report
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