2-dineusional couformal field theory and subfactors

2-离散共形场理论和子因子

基本信息

批准号：
11640214
负责人：
HIDEKI Omori
金额：
$ 2.18万
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：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

In this term. it is getting clear that the mathematical research of quantum physic is not a research of physic, but a research of the way of recognition of the quantum world, or the research for finding new concept which express correctly the quantum world.In this direction, we propose a new mathematical notion, p-regulated algebras which includes the notion of formal deformation quantization and quasntizations where h is not treated as a formal parameter.In an extension of such algebras where h is not treated as a formal parameter, we lined several anomalous fact such as a single element has two different inverses, or has left inverse a right inverse at the same time. These phenomena show taht the associativity breaks down in such extended object. In order to avoid such anomalous phenomena, one has to break some symmetry by complex multiplication, and one has to restrict. the whole system in the coefficients of real numbers.Moreover, the "group" generated by the *-exponential functions of quadratic forms be haves as if it were the non-tivial double cover of SL(2 ; C), which is simply connected. Here the notion of "point" is by no means a absolute notion, but only a local notion. This seems to correspond that an individual electron has a meaning in only a very restricted situation.To make such "anomalous phenomena" an "ordinary phenomena" in the quantum world one has to invent some new way of recognition, which must be a very now experiance of mathematics

在这个学期。显然，量子物理学的数学研究不是对物理的研究，而是对识别量子世界的识别方式的研究，或者是找到正确表达量子世界的新概念的研究。在这个方向上，我们提出了一个新的数学概念，提出了一个正式量化和Quasterizatize的概念，其中包括正式化和quasterizatize的概念，而不是在其中，而不是在其中，而不是正式的量子，则是一个正式的量子。 h不被视为形式参数，我们列出了几个异常事实，例如单个元素具有两个不同的倒置，或者同时使右逆倒不相反。这些现象表明，这种扩展对象中的关联分解。为了避免这种异常现象，必须通过复杂的乘法破坏一些对称性，并且必须限制。更重要的是，由二次形式的 * - 指数函数生成的“组”的整个系统就像是仅连接的SL（2; C）的非同意双重覆盖。在这里，“点”的概念绝不是绝对的概念，而只是当地的概念。这似乎是一个单个电子在非常有限的情况下具有含义的意义。要使这种“异常现象”成为量子世界中的“普通现象”，一个人必须发明一些新的识别方式，这一定是现在的数学经验