1996 Fiscal Year Final Research Report Summary
Quantum field theory and the connected differential geometry
| 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)
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| Project Period (FY) |
1994 – 1996
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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 |
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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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