Symmetry in Noncommutative Geometry and its String Theory Origin

非交换几何中的对称性及其弦理论起源

• 批准号: 19540257
• 负责人: WATAMURA Satoshi
• 金额: $ 2.83万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540257/
• 关键词: 素粒子理論; 数理物理; 幾何学; 非可換幾何学; 弦理論; 素料子理論

Summary of the results of the research : It became apparent that the structure of the Hopf algebra as a symmetry of the string theory and the structure of the deformation of the operator algebra caused by the existence of the non-trivial B-field background can be unified under the 'twist quantization', which is proposed by us and applied for the formulation of the string world sheet quantization by the twist element of the Hopf algebra, in the way that the deformation of operator algebra occurs due to the quantization and the deformation by B-field background are constructed in the single deformation of the same level. It means that in the string level, the Hopf algebra which contains the diffeomorphism in string theory, is deformed by both quantization and B-field background into the quantum group algebra including the deformed diffeomorphism.

研究结果总结：很明显，作为弦论对称性的Hopf代数的结构和由于非平凡B场背景的存在而引起的算子代数变形的结构可以在我们提出的“扭曲量化”下统一起来，并应用于通过Hopf代数的扭曲元素来表述弦世界片量化，其方式为： 算子代数的发生是由于量化而发生的，并且B场背景的变形是在同一级别的单个变形中构造的。这意味着在弦层面，弦论中包含微分同胚的Hopf代数在量子化和B场背景的共同作用下变形为包含变形微分同胚的量子群代数。

项目成果

Nahm変換と境界状態のT-duality

Nahm 变换和边界态 T 对偶性

• 发表时间: 2010
• 作者: 手島芳郎;浅川嗣彦;綿村哲;U.C-Watamura
• 通讯作者: U.C-Watamura

Hopf Algebra Symmetry and String Theory

霍普夫代数对称性和弦理论

• 发表时间: 2008
• 期刊: Prog.of Theor.Phys. 120
• 作者: A. Tsuguhiko;M. Mori;S. Watamura
• 通讯作者: S. Watamura

Instantons in Non(anti)commutative Gauge Theory via Deformed ADHM Construction

通过变形 ADHM 构造的非（反）交换规范理论中的瞬子

• 发表时间: 2008
• 期刊: Noncommutative geometry and physics 2005 1
• 作者: T. Araki;T. Takashima;S. Watamura
• 通讯作者: S. Watamura

A Hopf algebra structure in String theory

弦论中的霍普夫代数结构

• 发表时间: 2007
• 作者: 手島芳郎;浅川嗣彦;綿村哲;U.C-Watamura;S. Watamura;S. Watamura;S. Watamura
• 通讯作者: S. Watamura

World Scientific(Noncommutative Geometry and physics 2005)

世界科学（非交换几何与物理2005）

• 发表时间: 2007
• 作者: U. Carow-Watamura;Y. Maeda;S. Watamura
• 通讯作者: S. Watamura