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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.江泽研究了量子霍尔（QH）系统，作为量子场论在非对易空间的应用。QH系统是一个平面电子世界，其中x和y坐标成为非对易的。当电子具有SU（N）对称性时，其代数结构成为W_∞代数的SU（N）扩张，他称之为W_∞（N）代数。由于非对易性，他证明了量子相干性是由电子之间的交换相互作用自发驱动的。通过观察与量子相干性相关的拓扑孤子，这一理论结果在实验上是可检验的。有趣的是，拓扑孤子是QH系统中的非对易孤子。作为主要结果之一，他通过对空穴态进行W_∞（N）旋转，构造了非对易孤子（skyrmion）的量子力学态。此外，还计算了单层QH系统和单层QH系统中Skyrmion的激发能， ...更多信息双层QH体系的理论计算结果与实验数据进行了比较。Watamura研究了从超弦理论中出现的非（反）对易空间上的规范理论中的非平凡组态。这一研究对于理解D-膜的性质具有重要意义。特别地，他利用投射模构造构造了一个非平凡的构形，Fuzzy球面上的n-丛。推广这种方法，他可以阐明同易CPn上的丛的结构。一方面，在4维空间中，可以通过使用所谓的ADHM构造来解决这个问题。然后，他将ADHM方法推广到非反对易超空间，并通过构造瞬子解来分析模空间。应用超场方法在这个问题上是一个开放的问题，即使在交换的情况下。他成功地构造了完全在超空间中的瞬子解，包括规范固定。他已经表明了变形的费米子和玻色子模空间对应的变形瞬子解决方案推广到nonanticommutative情况。少

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

N.Kumada: "Effects of In-plane Magnetic Fields on Spin Transitions in Bilayer Quantum Hall States"Physica E. (印刷中). (2003)

N.Kumada：“平面内磁场对双层量子霍尔态自旋跃迁的影响”Physica E.（出版中）。