| Project/Area Number |
16H03942
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
宮尾 忠宏 北海道大学, 理学研究院, 准教授 (20554421)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥14,950,000 (Direct Cost: ¥11,500,000、Indirect Cost: ¥3,450,000)
Fiscal Year 2019: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2018: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
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| Keywords | 基底状態 / くりこみ / 場の量子論 / 汎関数積分 / ギブス測度 / 準古典近似 / 自己共役性 / 熱半群 / ファインマン・カッツ公式 / Gibbs測度 / スペクトル解析 / 自己共役作用素 / 経路積分 / くりこみ理論 / ファインマンカッツ公式 / ローレンツ多様体 |
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| Outline of Final Research Achievements |
A. Construction and application of Gibbs measure by rough path theory, B. Ground state study, C. Stochastic UV renormalization, D. Study of quantum field theory on manifolds, E. Study of SDE and semi-classical limit in quantum field theory. In addition, every other year, an international workshop on spectral analysis of quantum field theory was held. Great progress has been made on A and C, and they are summarized in a paper. The results of B were also summarized and completed as a paper. Regarding E, joint research has begun and research is ongoing. Every year, I was able to support travel expenses for the holding of international research meetings.
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| Academic Significance and Societal Importance of the Research Achievements |
数学的な場の量子論のスペクトルの研究で汎関数数積分を応用し、非摂動的な手法を切り開いた。E.Nelsonが未完成で終えた確率解析的なくりこみ理論を完成させ、さらに基底状態の性質を調べることができた。また、研究集会では大学院生など若い世代の研究者に旅費等の支援を行い参加を促した。
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