2013 Fiscal Year Final Research Report
Applications of Renormalization Group Methods in Mathematical Sciences
| Project/Area Number |
23540257
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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 |
Global analysis
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| Research Institution | Setsunan University |
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Principal Investigator |
ITO Keiichi 摂南大学, 理工学部, 教授 (50268489)
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| Co-Investigator(Kenkyū-buntansha) |
TERAMOTO Toshiaki 摂南大学, 理工学部, 教授 (40237011)
宮尾 忠宏 摂南大学, 理工学部, 講師 (20554421)
宮尾 忠宏 北海道大学, 自然科学研究科, 准教授 (20554421)
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| Co-Investigator(Renkei-kenkyūsha) |
TAMURA Hiroshi 金沢大学, 機械工学系, 教授 (80188440)
HIROKAWA Masao 岡山大学, 自然科学研究科, 教授 (70282788)
HIROSHIMA Funio 九州大学, 数理学研究科, 准教授 (00330358)
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| Project Period (FY) |
2011 – 2013
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| Keywords | くりこみ群 / ミレニアム問題 / シグマ模型 / 格子ゲージ模型 / くりこみ群の流れ |
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| Research Abstract |
We applied the renormalization group methods to the longstanding problems (the so-called Millennium problems) in mathematical sciences which go back to the last century. We apply this method to solve the 2D O(N) symmetric spin model which is a prototype model of the gauge theory model. In this model, one needs to integrate over infinite variables which form a functional space. We find a set of subspaces (called flow) which dominate the integral. This enables us to solve the recursive integrals and obtain the final result.
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