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Deformation quantization and noncommutative geometry

变形量化和非交换几何

基本信息

批准号：
15540094
负责人：
YOSHIOKIA Akira
金额：
$ 2.3万
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：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540094/
关键词：
Deformation quantization Star product Symplectic geometry Quantization Hamiltonian mechanics Hamiltonian mechanics gerbe Lie group Deformation Quantization gerb Deformation quantizalion Hamiltonia mechanics

项目摘要

By means of a complex symmetric matrix K, we have a linear isomorphism from the Weyl algebra to the space of all polynomial P(C,2n). We introduce a topology into the space P(C,2n) with respect to which the induced product is smooth, and we can take the completion. The star exponential belongs to the complete space. We investigate the two constructions of the star exponential function of the quadratic forms in P(C,2n). One is given by the path integral methods and the other is given by solving an ordinary differential equation. We investiageted the associated bundle structure over the space of symmetric matrices. We also investigate the noncommutative complex projective space given by convergent star products. In future we will study the extended concept of bundle structure which naturally enters through convergent star product algebras.

借助于复对称矩阵K，我们得到了从Weyl代数到所有多项式空间P(C，2n)的线性同构。我们在P(C，2n)空间中引入一个拓扑，它的诱导积在其上是光滑的，并且我们可以取它的完备性。恒星指数属于完备空间。研究了P(C，2n)中二次型的星指数函数的两种构造方法。一种是用路径积分法给出的，另一种是通过解一个常微分方程组给出的。我们研究了对称矩阵空间上的伴随丛结构。我们还研究了由收敛星积给出的非对易复射影空间。在未来，我们将研究通过收敛星积代数自然进入的丛结构的扩展概念。

项目成果

期刊论文数量（59）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

On vectorial gerbes and Poincare-Cartan classes

关于矢量非洲菊和庞加莱-嘉当类

DOI：
发表时间：
期刊：
Proceedings in Noncommutative geometry and Physics (World Scientific) (To appear)
影响因子：
0
作者：
Yoshiaki Maeda;Naoya Miyazaki;Hideki Omori;Akira Yoshioka;Tamio Hara;宮崎直哉;Naoya Miyazaki;Akira Yoshioka;Hideki Omori;Yoshiaki Maeda;Atushi Inoue;Yoshiaki Maeda;Tamio Hara;Tamio Hara;Tamio Hara;Akira Yoshioka;Hideki Omori et al.;Yoshiaki Maeda;Tamio Hara;Naoya Miyazaki
通讯作者：
Naoya Miyazaki

A.Yoshioka, T.Matsumoto: "Path integral star exponential functions of quadratic forms"Geometry, Integrability and Quantization, I.Mladenov G.Naber ed.. 4. 330-340 (2003)

A.Yoshioka、T.Matsumoto：“二次形式的路径积分星指数函数”几何、可积性和量化，I.Mladenov G.Naber ed.. 4. 330-340 (2003)