Topological Field Theory and Superfluid Thin Film

拓扑场论与超流薄膜

• 批准号: 04804024
• 负责人: ICHINOSE Ikuo
• 金额: $ 1.15万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04804024/
• 关键词: 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

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.

目前的研究表明，二维阿贝尔希格斯模型在某个参数区域成为拓扑场论，并且在另一个参数区域包含XY模型，是一种有效的超流薄膜理论。今年，我们用重正化群的方法研究了阿贝尔希格斯模型，阐明了该模型的整体结构，特别是拓扑激发和自旋波的行为。为此，找出阿贝尔希格斯模型等同于大规模正弦戈登模型这一事实至关重要。然后利用通常动量截止的重正化群方法研究了大规模正弦-Gordon模型，并用数值方法得到了递推方程组的解。解表明重整化群有两条固定线。一个对应于XY模型的低温相，另一个对应于拓扑场相。作为今年获得的另一个结果，我们证明了阿贝尔希格斯模型相当于具有四费米相互作用的二维QED。根据阿贝尔希格斯模型的知识，阐明了该理论的真空结构并明确计算了相关函数。

项目成果

I.Ichinose,H.Mukaida: "Renormalization-Group Study of the Massive Sine-Gordon Theory and Phase Structure of the Abelian Higgs Model" Int.J.Mod.Phys.A. (発表予定).

I.Ichinose、H.Mukaida：“阿贝尔希格斯模型的大规模正弦戈登理论和相结构的重正化群研究”Int.J.Mod.Phys.A（待提交）。

I.Ichinose 他: "Operator Solution of the Schwinger-Thirring Mode1 by the Abelian Higgs Boson" Anm.Physics. (発表予定).

I.Ichinose 等人：“阿贝尔希格斯玻色子的 Schwinger-Thirring 模式 1 的算子解”Anm.Physics（待提交）。

Ikuo Ichinose: "The U(1) gauge-Higgs model in two dimeusious and to pological field theory" Nuclear Physics B. B375. 318-340 (1992)

Ikuo Ichinose：“两个微弱场论和拓扑场论中的 U(1) 规范希格斯模型”核物理 B. B375。

I.Ichinose & H.Mukaida: "Renormalization-Group Study of the Massire Sine-Gordon Theory and Phase Structure of the Abelian Higgs Model" Int.J.Mod.Phys.A. (in press).

一之濑一

Ikuo Ichinose: "The massive sine-Gordon theory and the Phase structure of the Abelian Higgs model" Nuclear Physics B.

Ikuo Ichinose：“大规模正弦戈登理论和阿贝尔希格斯模型的相结构”核物理 B.