| Project/Area Number |
20340032
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
HIROSHIMA Fumio Kyushu University, 大学院・数理学研究院, 准教授 (00330358)
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| Co-Investigator(Renkei-kenkyūsha) |
ITOU Keiichi 摂南大学, 工学部, 教授 (50268489)
HIROKAWA Masao 岡山大学, 大学院・自然科学研究科, 教授 (70282788)
MATSUI Taku 九州大学, 大学院・数理学研究院, 准教授 (50199733)
NAKANO Fumihiko 学習院大学, 理学部, 教授 (10291246)
OBATA Nobuaki 東北大学, 大学院・情報科学研究科, 教授 (10169360)
HATTORI Tetsuya 慶応大学, 経済学部, 教授 (10180902)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2010: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2009: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2008: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
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| Keywords | 場の量子論 / 無限次元解析 / 散乱理論 / スペクトル解析 / 汎関数積分 / 基底状態 / 半群 / 確率過程 / 1パラメター半群 / レヴィー過程 |
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| Research Abstract |
Ground states of quantum interaction systems are investigated. By means of functional integral representations quantum systems are studied in non-perturbative way. We show the existence and absence of ground states of the so-called Nelson model defined on a Lorentz manifold, we remove the UV cutoff by means of micro-local analysis. The asymptotic completeness of the Pauli-Fierz model defined on an indefinite Hilbert space is also established. We investigate enhanced bindings. We specify the no-binding regime of the Pauli-Fierz model and show the enhanced binding of the relativistic Nelson model. We next consider functional integrations. The heat semi-group generated by the relativistic Schroedinger operator with spin 1/2 is represented in terms of Brownian motions, Poisson processes and subordinators. By this we can derive a non-trivial energy comparison inequality. Moreover we extend this path integral representation to the Bernstein functions of the Laplacian, and apply this to a spin-boson model to show the uniqueness of the ground state. We furthermore succeeded to construct an infinite volume limit of the Gibbs measure with double stochastic integral as potential.
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