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Grassmann algebra with half infinite forms and its applications to the global analysis of mapping spaces

半无限形式的格拉斯曼代数及其在映射空间全局分析中的应用

基本信息

批准号：
10640202
负责人：
ASADA Akira
金额：
$ 1.02万
依托单位：
Shinshu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640202/
关键词：
Spectre triple Zeta-regularization Dirac operator Soboler space Cohen-Macauley AKNS inverse Minkowski space motion of curves Spectre triple Zeta-regularization Sobolev space AKNS inverse scattering schemes Minkowski space Mapping

项目摘要

1. Regularization of differential operation on a Halberd space.Considering the pair of a Hilbert space H and some Kinds of Schatten class operator G on H, we propose a regularization of differential operators on H by using spectuer of G. We compile proper values and functions of regularized Loplacian and Dirac operator with suitable boundary conditions. We also clarify the meaning of zeta regularization and the relation of zeta regularization and infinite spinor adgoisred to the Cli Hord algebra over H by using this result.2. Zeta regularized determinant of differential operators.We solved a problem presented by Elizalde on the zeta regularized determinant of Dirac operators with mass-terms and give the relation between the sign of zeta regularized determinant and mass-term.3. Study on Cohen-Macauley algebras.Nisida studied algebras related to the thema of this project. Especially on the minimal injective resolution and Catenary and well studied.4. Study on integrable equations.Nakayama showed all integrable equations by the AKNS inverse scattering schemer are obtained from the movement of curves in a hyperboloid in the Minkowski space and gene its group theoretical reason.

1. Halberd 空间上微分算子的正则化。考虑到 Hilbert 空间 H 和 H 上的几种 Schatten 类算子 G，我们提出了利用 G 的镜谱对 H 上的微分算子进行正则化。我们在适当的边界条件下编译了正则化 Loplacian 和 Dirac 算子的适当值和函数。利用这个结果我们还阐明了zeta正则化的含义以及zeta正则化与H上的Cli Hord代数的无限旋量的关系。 2．微分算子的zeta正则行列式。我们解决了Elizalde提出的带质量项的狄拉克算子zeta正则行列式问题，并给出了zeta正则行列式的符号与质量项的关系。 3． Cohen-Macauley 代数的研究。Nisida 研究了与该项目主题相关的代数。特别是对最小单射分辨率和悬链线问题进行了深入研究。 4．可积方程的研究。Nakayama 证明了 AKNS 逆散射方案器的所有可积方程都是从 Minkowski 空间中双曲面上的曲线运动获得的，并基因其群理论原因。