| Project/Area Number |
04804024
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | University of Tokyo |
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Principal Investigator |
ICHINOSE Ikuo College of Arts and Science, Associate Professor, 教養学部, 助手 (20159841)
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| Co-Investigator(Kenkyū-buntansha) |
簔口 友紀 東京大学, 教養学部, 助手 (10202350)
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| Project Period (FY) |
1992 – 1993
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| Project Status |
Completed (Fiscal Year 1993)
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| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1993: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1992: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | renormalization group / topological field theory / K-T transition / sine-Gordon theory / K-T転移 / 位相的励起 / XYモデル / サイン・ゴルドン理論 |
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| Research Abstract |
Present study showed that the 2-dimensional Abelian Higgs model becomes a topological field theory at some parameter region, and also it containes the XY model at another parameter region, which is an effective theory for superfluid thin film. In the present year, we studied the Abelian Higgs model by a method of the renormalization group, and clarified the global structure of this model, especially the behavior of the topological exciations and the spin wave. To this end, it was crucial to find out the fact that the Abelian Higgs model is equivalent to the massive sine-Gordon model. Then the massive sine-Gordon model was studied by the renormalization-group method with the usual momentum cut off, and solutions to the recursion equations were obtained by numerical method. The solutions show that there are two fixed line of the renormalization group. One corresponds to low-temperature phase of the XY model and the other is the topological-field phase.
As another result obtained this year, we proved that the Abelian Higgs model is equivalent to the 2-dimensional QED with the four-fermi interaction. From the knowledge of the Abelian Higgs model, the vacuum structure of this theory was clarified and correlation functions were explicitly calculated.
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