Quantum Field Theory on Noncommutative Space and Its Applications

作为量子场论在非对易空间上的应用，Z.F.Ezawa对量子霍尔系统进行了研究。QH系统是一个平面电子的世界，其中x和y坐标变得非对易。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，他已经证明了量子相干性是由电子之间的交换相互作用自发产生的。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验证的。有趣的是，在QH系统中，拓扑孤子是一种非对易孤子。作为主要结果之一，他通过使空穴状态W_∞(N)旋转来构造非对易孤子(天空)的量子力学状态。此外，在单层QH系统和…中都计算了天空离子的激发能S.Watamura研究了规范理论中的非平凡组态在超弦理论中出现的非(反)对易空间。这项研究对于了解D-膜的性质很重要。特别地，他利用射影模构造法构造了一种非平凡构形--模糊球面上的单极子丛。推广这一方法，他可以澄清交换CPN上丛的结构。一方面，在4维空间中，可以用所谓的ADHM结构来解决这一问题。然后，他将ADHM方法推广到非对易超空间，并通过构造瞬子解来分析模空间。即使在对易的情况下，将超场方法应用于这个问题也是一个开放的问题。他已经成功地在超空间中完全构造了瞬时解，包括规范的确定。他展示了费米子和玻色子模空间的变形，对应于推广到非对易情况的变形瞬子解。较少

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