Topological Field Theory and Superfluid Thin Film
Project/Area Number  04804024 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
物理学一般

Research Institution  University of Tokyo 
Principal Investigator 
ICHINOSE Ikuo College of Arts and Science, Associate Professor, 教養学部, 助手 (20159841)

CoInvestigator(Kenkyūbuntansha) 
簔口 友紀 東京大学, 教養学部, 助手 (10202350)

Project Fiscal Year 
1992 – 1993

Project Status 
Completed(Fiscal Year 1993)

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)

Keywords  renormalization group / topological field theory / KT transition / sineGordon theory / くりこみ群 / 位相場の理論 / KT相移 / sineGordon理論 / KT転移 / 位相的励起 / XYモデル / サイン・ゴルドン理論 
Research Abstract 
Present study showed that the 2dimensional 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 sineGordon model. Then the massive sineGordon model was studied by the renormalizationgroup 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 lowtemperature phase of the XY model and the other is the topologicalfield phase. As another result obtained this year, we proved that the Abelian Higgs model is equivalent to the 2dimensional QED with the fourfermi interaction. From the knowledge of the Abelian Higgs model, the vacuum structure of this theory was clarified and correlation functions were explicitly calculated.

Report
(4results)
Research Output
(10results)