Quantum Field Theory on Noncommutative Space and Its Applications

非交换空间的量子场论及其应用

基本信息

批准号：
13135202
负责人：
EZAWA Zyun F.
金额：
$ 10.18万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2006
项目状态：
已结题

项目摘要

Z. F. Ezawa made an investigation on quantum Hall (QH) systems as an application of the quantum field theory on noncommutative space. The QH system is a world of planar electrons, where the x and y coordinates become noncommutative. When the electron possesses the SU(N)symmetry,the algebraic structure becomes the SU(N)extension of the W_∞ algebra,which he has named the W_∞(N)algebra. Due to the noncommutativity he has shown that quantum coherence develops spontaneously driven by the exchange interaction between electrons. This theoretical result is experimentally testable by observing topological solitons associated with the quantum coherence. It is intriguing that the topological soliton is a noncommutative soliton in QH systems. As one of the main results, he has constructed the quantum mechanical state of a noncommutative soliton (skyrmion) by making a W_∞(N)rotation of a hole state. Furthermore, calculating the excitation energy of a skyrmion both in the monolayer QH system and the … More bilayer QH system, he has compared successfully his theoretical results with the experimental data.S. Watamura has studied non-trivial configurations in the gauge theory on the non-(anti)commutative spaces which are emerging from the superstring theory. This research is important to understand the properties of a D-brane. Especially, he has constructed a non-trivial configuration, the monopole bundle on the Fuzzy sphere by using the projective module construction. Generalizing that method, he could clarify the structure of the bundles on concommutative CPn. On the one hand, in 4-dimensional space one can solve this problem by using the so-called ADHM construction. He then generalized the ADHM method to the non-anticommutative superspace and analyzed the moduli space by constructing the instanton solutions. Applying the superfield method on this problem was an open problem even in the commutative case. He has succeeded to construct the Instanton solutions completely in the superspace, including the gauge fixing. He has shown the deformation of the fermionic and bosonic moduli space corresponding to the deformed instanton solution generalized to the nonanticommutative case. Less

Z. F. Ezawa对Quantum Hall（QH）系统进行了投资，作为量子场理论在非交通空间上的应用。 QH系统是平面电子的世界，X和Y坐标变得不交流。当电子具有SU（N）对称性时，代数结构将变成W_∞代数的SU（N）延伸，他将其命名为W_∞（N）代数。由于不交流性，他表明量子相干性由电子之间的交换相互作用驱动。通过观察与量子相干性相关的拓扑结构，可以在实验上测试该理论结果。令人着迷的是，拓扑固体是QH系统中的非共同固体。作为主要结果之一，他通过使孔状态的W_∞（N）旋转构建了非交通固体（Skyrmion）的量子机械状态。此外，在单层QH系统和…更多的双层QH系统中，计算Skyrmion的兴奋能量，他将其理论结果成功地与实验数据进行了比较。 Watamura研究了仪表理论中的非平凡构型，这些构型是从超弦理论中出现的非（反）交换空间。这项研究对于了解D-Brane的特性很重要。尤其是，他通过使用射影模块的构造构建了一种非平凡的配置，即模糊球体上的单极束。概括该方法，他可以阐明捆绑CPN上的捆绑包结构。一方面，在四维空间中，可以使用所谓的ADHM结构来解决此问题。然后，他将ADHM方法概括为非通用的超空间，并通过构建激体溶液分析了模量空间。即使在交换案件中，在此问题上应用超场方法也是一个悬而未决的问题。他成功地在超空间中完全构建了激体解决方案，包括量规修复。他已经显示了对应于对非通用情况的变形液体溶液对应的费米和骨气模量空间的变形。较少的

项目成果

期刊论文数量（92）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Monopole Bundles over Fuzzy Complex Projective Spaces

模糊复射影空间上的单极子束

DOI：
发表时间：
2005
期刊：
Journal of Geometry and Physics 54
影响因子：
0
作者：
A.Higuchi;Y.Higuchi;K.Furuta;B.O.Yoon;M.Hara;S.Maniwa;M.Saitoh;K.Sanui;U. Carow-Watamura
通讯作者：
U. Carow-Watamura

Z.F.Ezawa: "Integer and fractional quantum Hall effects in Bilayer Electron Systems"J. Phys. Chemi. Solids. (印刷中). (2002)

Z.F.Ezawa：“双层电子系统中的整数和分数量子霍尔效应”，《化学固体》（出版中）。