| Project/Area Number |
22654018
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
SASAKI Itaru 信州大学, 総合工学系研究科, 助教 (50558161)
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| Project Period (FY) |
2010 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥1,940,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 関数解析 / 場の量子論 / 無限次元解析 / スペクトル散乱理論 / スペクトル解析 / 汎関数積分 / 基底状態 / レヴィー過程 / シュレディンガー作用素 / 散乱理論 / 半群 / 確率過程 |
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| Research Abstract |
According to purpose(I),(II) and(III) proposed in KENKYU-KEIKAKU-CHOSHO, we review results obtained by Grant-in-Aid for Challenging Exploratory Research.
(I) The functional integral representation of the heat semi-group generated by the relativistic PF model is constructed in terms of three stochastic processes, Euclidean field, Brownian motion and subordinator. By using this we show the essential self-adjointness of PF model, decay of bound states and the uniqueness of ground state.
(II) Enhanced binding of the many-body relativistic Nelson model is shown with Itaru Ssasaki(Shinshu university). A functional integral representation is a key ingredient. The result was sent to an international journal for publication.
(III) The Nelson model defined on a pseudo Riemannian manifold is studied with C. Gerard(Paris XI), Akito Suzuki(Shinshu university) and Annalisa Panati(Toulon-Var). We published papers in international journals.
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