2009 Fiscal Year Final Research Report
Quantization of difference nonlinear equation of Painleve type
| Project/Area Number |
19540207
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
HASEGAWA Koji Tohoku University, 大学院・理学研究科, 講師 (30208483)
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| Co-Investigator(Renkei-kenkyūsha) |
KUROKI Gen 東北大学, 大学院・理学研究科, 助教 (10234593)
KIKUCHI Tetsuya 東京大学, 大学院・数理科学研究科, 特任研究員 (00374900)
NAGOYA Hajime 東京大学, 大学院・数理科学研究科, 特任研究員 (80447367)
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| Project Period (FY) |
2007 – 2009
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| Keywords | パンルヴェ方程式 / ソリトン系 / 対称性 / 量子群 / 量子化 / 差分化 |
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| Research Abstract |
Panleve equations are second order nonlinear ordinary differential equations with certain good properties discovered in early 1900s. They are nonautonomous Hamiltonian systems allowing affine Weyl group symmetry, arise from monodromy preserving equations as well as solitonic partial differential equations through dimensional reduction. Painleve type equations are those equations with high symmetry, partial or of higher order in general, arising in similar ways. We investigate the canonical quantization of Painleve type equations and difference versions thereof. In particular we gave the quantized difference Painleve equations via the reduction of quantized solitonic systems, as well as the formulation as generalization of conformal field theories.
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