| Project/Area Number |
18K03286
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
YOSHIOKA Akira 東京理科大学, 理学部第二部数学科, 客員教授 (40200935)
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 変形量子化 / 変形量子化代数の指数関数 / convergent star product / 変形量子化の応用 / star Mittag-Leffler / star Kummer function / star gamma function / star zeta function / star積 / gamma関数 / zeta関数 / 関数の変形 / star積の代数 / star積に関する指数関数 / 発散級数 / Kummer関数 / SU(2)ケプラー問題 / Mittag-Leffler関数 / 指数関数の量子変形 / 変形量子化関数 / 超幾何関数の変形 / 非可換幾何学 / 非可換シュワルツシルド宇宙 / 拡張不確定性関係 / 中心配置 / 非可換指数関数 |
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| Outline of Final Research Achievements |
Deformation quantization is to deform the usual product of functions into an associative product. The deformed product is called the star product. Using star products, we have constructed deformation of several functions and obtained the functional equations which the deformed functions satisfy. In particular, we study the deformation of exponential functions and has found that the exponential function has singular points and clarified some of its properties. The strength of the calculation of deformation quantization is that it is elementary and direct, and then, in terms of applications, it has been able to demonstrate its power in calculations of physical models. Applying it to a concrete cosmological model, we presented a formula that calculates the quantum mechanical uncertainty relation to the order of the square of Planck's constant. We also calculated eigenvalue problems in quantum mechanics.
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| Academic Significance and Societal Importance of the Research Achievements |
学術的な意義として、（１）量子計算の様々な関係式を、作用素ではなく関数を用いた初等的・直接的な式に表すこと、（２）様々な概念の非可換化を行う解析的・幾何学的な方法を与えること、の２点を挙げることができる。社会的意義として、積が具体的な表示式により与えられることから、物理学・化学および工学における量子的な計算を、作用素ではなく関数のべき級数展開を用いて直接的かつ初等的に行うことが可能であり、将来、具体的な問題の解決に役に立つことが期待される点を挙げることができる。
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