2014 Fiscal Year Final Research Report
Path integral approach to quantum mechanical propagators
| Project/Area Number |
23540191
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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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| Research Field |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAMURA Hideo 岡山大学, 自然科学研究科, 特命教授 (30022734)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | 関数方程式 / 経路積分 / プロパゲイター / トロッター積公式 / トロッター・加藤積公式 / 相対論的シュレーディンガー作用素 / レヴィ過程 / アハラノフ・ボーム効果 |
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| Outline of Final Research Achievements |
This research deals with the quantum-mechanical propagator, namely, the integral kernel of the Schroedinger unitary group, Green function as well as the heat kernel of the Schroedinger semigroups as its imaginary-time version. In this work, among others, we have considered three different magnetic relativistic Schroedinger semigroups and establish (imaginary-time) path integral representations with the probability measure on the path space connected with the Levy process to clarify their different nature.
Some other topics are also dealt with on influence to resonance of Aharanov-Bohm effect for solenoidal magnetic field quantum mechanical scattering, and on an improved Sobolev inequality for vector-valued functions whose right-hand side has a seminorm involving Dirac operator.
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| Free Research Field |
関数方程式
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