2007 Fiscal Year Final Research Report Summary
Mathematical Foundation of the Renormalization Group Methods and its Applications in Mathematical Sciences
| Project/Area Number |
17540208
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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 | Setsunan University |
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Principal Investigator |
ITO Keeichi Setsunan University, Departmrnt of Mathematics and Physics, Professor (50268489)
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| Co-Investigator(Kenkyū-buntansha) |
ONO Hiroaki Setsunan University, Departmrnt of Mathematics and Physics, Professor (50100780)
TERAMOTO Yoshiaki Setsunan University, Departmrnt of Mathematics and Physics, Associate Professor (40237011)
SHIMADA Shin-ichi Setsunan University, Departmrnt of Mathematics and Physics, Associate Professor (40196481)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Renormalization Group / Phase Transition / Critical Phenomena / Non-linear PDE / fluid mechanics / turbulence / Para Statistics / Pauli-Fiertz Model |
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| Research Abstract |
Ito investigates the Pauli-Fierz model (classical quantum electrodynamics) with Dr. F.Hiroshima and showed that the divergence of mass term is so strong that the model is not renomalizable though the original model is renormalizable. The reasons are discussed.
He also worked with Prof. H. Tamura of Kanazawa University on the relations between point processes and statistics of particles. This study based on the work by Takahashi and Shirai, and showed that some series of point processes are equivalent to para-partcles which obey para-statistics. Moreover they could establish Bose-Einstein condensation within this frame.
Ito also worked with Dr.F.Hiroshima and Dr.M.Kuse on non-linear evolution equations which appear in the continuum limit (Wegner-Houghton-Aoki approximation) of block spin transformation
Moreover Ito worked with Prof.E.Seiler on the problem of quark confinement. Ito proved a permanent Quark confinement on 4D hierarchical lattices of Migdal-Kadanoff type. It was very hard to do the same real lattice space. So we argued if it was possible to extend our argument to the real system. The result is so far negative.
Teramoto investigated imcompressive viscous flow down an inlined plane, together with Professor T.Nishida. He also considered the bifurcation theorems for the model system of Bernard-Marangoni Convection
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