Reseach of non commutative geometry

非交换几何研究

• 批准号: 14540092
• 负责人: OMORI Hideki
• 金额: $ 2.11万
• 依托单位: TOKYO UNIVERSITY OF SCIENCE
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540092/
• 关键词: Non-commutative Geometry; Star-product; Deformation quantization; *-積; 量子化

In the transcendently extended Weyl algebra, there was no systematic theory of intertwiners. This research attempt to construct a systematic theory for these. Here is the summary of facts, uncovered by the research :1)Existence of multi-valued elementsThis is observed as monodromy phenomena for the parallel translation by infinitesimal intertwiners. That is, even though the parameter of expression came back to the starting point, the parallelly translated element did not come back to the starting point.2)Group-like object which does not form a point setThis is viewd as a model regarded as a non-trivial double covering group of a "simply connected" Lie group.In the traditional mathematics, such an object is logically impossible. However, it is permitted to exist, because of the existence of multi-valued elements.3)Manifolds patched by multi-valued coordinate transformationsMulti-valued functions are familiar in classical mathematics. However, there was no notion of manifolds, which are understood as a patchwork of local coordnate neighborhoods by multivalued coordinate transformations. Such notions are required to understand the phenomena mentioned above.

在超越扩张的Weyl代数中，没有系统的缠绕子理论。本研究试图为这些问题构建一个系统的理论。1）多值元素的存在性这是由无穷小纠缠器并行平移的单值现象。2）不构成点集的类群对象这是一个被看作“单连通”李群的非平凡双覆盖群的模型，在传统数学中，这样的对象在逻辑上是不可能的。3）多值坐标变换修补流形多值函数在经典数学中是常见的。然而，没有流形的概念，流形被理解为通过多值坐标变换的局部坐标邻域的拼凑。这些概念是理解上述现象所必需的。

项目成果

数学の中の物理学

数学中的物理

• 发表时间: 2004
• 作者: H.Omori;Y.Maeda;N.Miyazaki;A.Yoshioka;大森英樹
• 通讯作者: 大森英樹

Star exponential functions for quadratic forms and polar elements

二次型和极元的星指数函数

• 发表时间: 2002
• 期刊: Contem.Math.A.M.S. 315
• 作者: H.Omori;Y.Maeda;N.Miyazaki;A.Yoshioka
• 通讯作者: A.Yoshioka

Associativity breaks down in deformation quantization

变形量化中关联性失效

• 发表时间: 2003
• 期刊: Advanced Studies in Pure Math. 37
• 作者: Hisao Kato;Eiichi;Matsuhashi;加藤久男;H.Omori
• 通讯作者: H.Omori

Star exponeutial functions for quadratic forms and polar elements

二次形式和极元的星型指数函数

• 发表时间: 2002
• 期刊: Contem.Math.A.M.S. 315
• 作者: H.Omori;Y.Maeda.N.Miyazaki;A.Yoshioka
• 通讯作者: A.Yoshioka

Associativity breaks down in deformation quntization

变形量子化中结合性失效

• 发表时间: 2002
• 期刊: Advanced Studies in Pure Math. vol 37
• 作者: H.Omori;Y.Maeda;N.Miyazaki;A.Yoshioka;H.Omori;H.Omori
• 通讯作者: H.Omori