| Project/Area Number |
03640099
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Nihon University |
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Principal Investigator |
SUZUKI Osamu The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (10096844)
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| Co-Investigator(Kenkyū-buntansha) |
MOTEGI Kimihiko The College of Humanities and Sciences, Nihon Univ., Department of Math., Lect.,, 文理学部, 講師 (40219978)
YAGUCHI Teruo The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (50059987)
NISHIOKA Kumiko The College of Humanities and Sciences, Nihon Univ., Department of Math., Asso., 文理学部, 助教授 (80144632)
SAKAI Shoichiro The College of Humanities and Sciences, Nihon Univ., Department of Math., Prof.,, 文理学部, 教授 (30130503)
SUZUKI Masahiko The College of Humanities and Sciences, Nihon Univ., Department of Math., Asso., 文理学部, 助教授 (00171249)
黒田 耕嗣 日本大学, 文理学部, 助教授 (50153416)
橘 貞雄 日本大学, 文理学部, 助教授 (70060035)
武笠 敏夫 日本大学, 文理学部, 教授 (00059750)
釜江 慶子 日本大学, 文理学部, 助教授 (60059566)
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| Project Period (FY) |
1991 – 1993
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| Project Status |
Completed (Fiscal Year 1993)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1991: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | gauge thery / flat extension therem / devergence in quantum field theory / Symmetry structure / algebroid / anomaly / 相転移 / K.M.S状態 / ゲージ接続 / 平坦拡張定理 / 非可変微分幾何 / 量子場の発散 / algebroid / 指数定理 / Gauss-Bonnet定理 / Singular pertuvbation / flat connection / Diff.eq.of Fuchsian Type / dynamical system / singular pertubation / constrained sysytem / quantum field theory / gauge connection / renormalization / anomaly / B.R.S.transformation |
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| Research Abstract |
A new formalism for gauge connections is given and monlinear gauge eauations are solved and the divergence of quantu field theory is discussed. The following results are obtained.
(1) A gauge theory is formulated in termas of a certain kind of a decomposition of a linear space, whitch is called a "gauge decomposition." Then every gauge connection connection can be extended to a flat connection, when it admits a representation in some algebra (flat extension theorem).
(2) By use of the result (1), nonlinear gauge equations can be solved by use of a decomposition of a solution of a linear equation. Symmetry structures and special class of silutions can be discussed as a "Galois thery for differntial equations". When it has a representation in "algebroids", divergece appears and anomaly and renormalization can discussed in this case.
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