| Project/Area Number |
26610020
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Ochanomizu University |
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Principal Investigator |
FURUYA Kiyoko お茶の水女子大学, 基幹研究院, 講師 (80189208)
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| Project Period (FY) |
2014-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 発展方程式 / 経路積分 / ディラック方程式 / ベクトル値測度 / 半群 |
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| Outline of Final Research Achievements |
The idea of Feynman's integral is a topic of great interest in mathematics and physics. But rigorous mathematical treatment of this integral is not enough. We defined a kind of operator-valued integration and define the path integrals.
Dirac equation is the basic equation of relativistic quantum mechanics to the fermions. For the case of space-dimension = 1, Ichinose proved the path integral for Dirac equations are represented by a scalar measure. For the case of radial Dirac equation Ichinose constructed a countably additive path space measure. But in general, for the case of space-dimension > 1, Feynman path integrals for Dirac equations are not represented by (scalar-valued) measures. We showed that the path integral for Dirac equations are represented by our vector-valued measure.
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