| Project/Area Number |
16540231
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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 |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Nihon University |
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Principal Investigator |
FUJIKAWA Kazuo Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (30013436)
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| Co-Investigator(Kenkyū-buntansha) |
NAKA Shigefumi Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (60120515)
DEGUCHI Shinichi Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (50207502)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Gauge symmetry / path integral / magnetic monopole / second quantization / geometric phase / holonomy / quantum anomaly / gauge field / 隠れたゲージ対称性 / 指数定理 / 電荷の量子化 / Q変形 / 位相 / トポロジー / 断熱近似 / 非可換時空 / ユニタリー性 / 摂動 / 真空状態 |
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| Research Abstract |
Fujikawa first examined the quantization of non-commutative space-time in the path integegral formulation, and showed that a modified time ordering prescription for space-time non-commutative theory, which preserves unitarity, inevitably breaks positive energy condition. He also studied the problem related to the small neutrino mass from a view point of the enhanced symmetry in the extended standard model when one sets the mass of the neutrino at zero.
Fujikawa together with Deguchi presented a second quantized formulation of geometric phases, which allows the treatment of the geometric phases in path integral and operator formalism equally well. The hidden local symmetry appearing in this formulation has been further studied by Fujikawa, and it was shown that all the geometric phases are understood as holonomy associated with this hidden exact local symmetry in the Schroedinger equation. This new formulation is consistent with the basic superposition principle of quantum mechanics as well as the gauge invariance requirement of all the physical observables. The geometric phases thus arise from the hidden local symmetry appearing in second quantization.
Deguchi studied the quantization of the magnetic monopole by using the Atiyah-Singer index theorem. Deguchi also studied the quantization of gauge filed on a sphere.
Naka clarified the Q-deformation and non-local field theories in general.
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