| Project/Area Number |
06640173
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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 | Nihon University |
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Principal Investigator |
SUZUKI Osamu Dep.Math.Nihon Univ.Professor, 文理学部, 教授 (10096844)
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| Co-Investigator(Kenkyū-buntansha) |
WATE Masamichi Dep.Math.Nihon Univ.Professor, 文理学部, 教授 (60059475)
橘 貞雄 日本大学, 文理学部, 教授 (70060035)
YAGUCHI Teruo Dep.Math.Nihon Univ.Professor, 文理学部, 教授 (50059987)
YAKU Takeo Dep.Math.Nihon Univ.Professor, 文理学部, 教授 (90102821)
SAKAI Shoichiro Dep.Math.Nihon Univ.Professor, 文理学部, 教授 (30130503)
武笠 敏夫 日本大学, 文理学部, 教授 (00059750)
鈴木 正彦 日本大学, 文理学部, 助教授 (00171249)
西岡 久美子 日本大学, 文理学部, 助教授 (80144632)
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| Project Period (FY) |
1994 – 1996
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| Project Status |
Completed (Fiscal Year 1996)
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| Budget Amount *help |
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1996: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1995: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1994: ¥400,000 (Direct Cost: ¥400,000)
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| Keywords | Hermitian Hurwitz pair / the siguature of the space time / Minkowski space / Riemann-Hilbent problem / regular singularities / vertex operator / Green kernel / dualities / Hurwifz対 / Yang-Mills場 / Riemann-Hilbert問題 / anormaly / Hurwitz pair / Clifford algebra / Dirac equation / gauge connection / Soliton equation / havmonic map / Yang-Mills field / アシュテカ理論 / ゲージ接続 / チャン・サイモン理論 / モノドロミ-表現 / リーマン・ヒルベルト問題 / フルヴィツ対 |
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| Research Abstract |
The subjects : The subjects are devided into two parts :
(1) Hermitian Hurwitz pairs and the sgnature problems of the space-time
(2) Divergence problems in quantum field theory and the Riemann-Hilbert problems
The results
(1) Hermitian Hurwitz pairs state some restriction on the sgnatures of the pseudo-Euclidean space. This leads us to the research on the sgnature problems of the space time. By use of the duality theorems, we consider the problem of 4 dimensional space-time. We obtain : (1,3) -space is equivalent to (2,2) -space by the Hurwitz duality and (1,3) -space is equivalent to (3,1) -space by use of the space-time duality. Hence, we have the only one space-time for 4-spaces.
(2) Divergences appear in the quantum field theory very often. We consider the geometry of divergence by use of the Riemann-Hilbent problems. The regular singularities are very important candidate, because of its closeduess and the relation to the Green komel. We formulate the quantum version of the R.-H.problem and solve it. We notice its expectation value becomes functions with regular singularities
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