权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Reserch on loop spaces related to mathematical physics

数学物理相关环空间研究

基本信息

批准号：
03640031
负责人：
ASADA Akira
金额：
$ 0.96万
依托单位：
Shinshu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1993
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640031/
关键词：
Loop spaces Loop group bundles Strlng classes WZNW terms Current group bundles Noncommutative connections Non-abelian de Rham theory Dirac operators GLpバンドル Upバンドル非可換曲率量子化ゴースト場ド・ラム型コホモロジー非可換チャーン類 η関数ル-プ空間ル-プ群ストリング数

项目摘要

(1) Research on loop group bundlesi. Characteristic map of a loop group bundle is realized as a matrix valued function.ii. Lifting and descent of a vector bundle or a loop group bundle over M to a loop group bundle or a vector bundle over OMEGAM or MXS^1 are defined.(2) Research on characteristic classes of loop group bundles (string classes)i. Differential geometric definition of string classes is given.ii. Relations between string classes and Chern classes of a bundle and its lifting or descent are computed.iii. String classes are expressed as WZNW terms of characteristic maps.(3) By using above results and non-abelian de Rham theory, relations between Chern-Simons gauge theory and topological field theory are studied.(4) To extend above results for loop groups over exceptiohal groups, concrete realizations of exceptional groups are done.(5) To get more advanced information in this direction, Eisenstein serieses of nurmber theoretical symmetric spaces are studied.(6) Research on current group bundles , I.Noncommutative connections. The notion of noncommutative connection is introduced and several results such as reduction to U_1-bundles and noncommutative Poincare lemma, are get.(7) Research on current group bundles, II.Connections with respect to the Dirac operator. Connections with respect to the Dirac operator is defined. They give families of Dirac operator and their n-functions give bundle invariants.

(1)循环群算法的研究。环群丛的特征映射被实现为矩阵值函数。定义了M上的向量丛或环群丛到OMEGAM或MXS ^1上的环群丛或向量丛的提升和下降。(2)循环群丛的特征类（串类）研究i.给出了弦类的微分几何定义.字符串类和陈类的一个丛和它的提升或下降之间的关系计算。字符串类表示为特征映射的WZNW项。(3)利用这些结果和非交换de Rham理论，研究了Chern-Simons规范理论与拓扑场论的关系。(4)为了推广上述结果，对例外群进行了具体的实现。(5)为了在这方面获得更进一步的信息，我们研究了数个理论对称空间的Eisenstein级数。(6)流群丛的研究I.非交换联络。引入了非交换联络的概念，得到了U_1-丛的约化和非交换Poincare引理等结果。(7)流群丛的研究II.与Dirac算子的联系。关于狄拉克算子的连接被定义。他们给出了Dirac算子的族和它们的n-函数给出了丛不变量。