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

Towards A New Formulation of Unified Model with Gravity on a Lattice

格子上重力统一模型的新表述

基本信息

批准号：
13640250
负责人：
KAWAMOTO Noboru
金额：
$ 2.37万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640250/
关键词：
Quantum Gravity Lattice Gravity Supersymmetry on the Lattice Twisted Supersymmetry Topological Field Theory Dirac-kahler Fermion Quantum gravity Super Yang-Mills Lattice SUSY Dirac-Kahler Fermion 超対称ゲージ理論ツイストされた超対称空間 N=2超対称性一般化

项目摘要

My research thema in this period can be classified into the following 4 categories :1)Continuation from the previous investigations.2)Fermion Formulation with Non-commutativity on a Lattice.3)A Proposal of New Superspace Formulation.4)Supersymmetry on a Lattice.1)Based on the generalized gauge theory formulation which we discovered, we applied a truncated version of generalized Yang-Mills theory with SU(2|1) gauge group and derived Weinberg-Salam model. Numerical evaluation of the c-dependence of the fractal dimension of two-dimensional quantum surface was investigated and the result is perfect agreement with the analytic result which we obtained previously.2)We may introduce mild non-commutativity for the lattice difference operator tosatisfy the Leibniz rule. We can then define differential form on a lattice and introduce associative Clifford product. We have clarified the Dirac-Kahler fermion formulation with non-commutativity on a lattice.3)It was already recognized that the twisting appeared in the quantization of topological field theory can be identified as a Dirac-Kahler fermion formulation. We found that this twisting mechanism is a universal characteristic which appears in the quantization of topological field theory and a twisted superspace formulation is hidden behind the formulation. N=2 twisted superspace formulation was formulated in two dimensions. Then this formulation is extended into N=4 in four dimensions.4)Twisted superspace formulation is successfully formulated on a lattice with the introduction of the mild non-commutatibity for N=2 twisted superspace in two dimensions. It is now possible to apply this formulation to N=2 super Yang-Mills action on a lattice.

我在这一时期的主要研究内容可以分为以下四个方面：1）对前人研究的继续; 2）格点上具有非对易性的费米子公式; 3）一个新的超空间公式的提出; 4）格点上的超对称性; 1）在我们发现的广义规范理论公式的基础上，应用SU（2）的广义Yang-Mills理论的截断形式|1）规范群和导出的Weinberg-Salam模型。数值计算了二维量子表面分维的c依赖性，结果与我们以前得到的解析结果完全一致。2）我们可以引入弱的非对易性来满足Leibniz规则。然后，我们可以在格上定义微分形式并引入结合Clifford积。3）拓扑场论量子化过程中出现的扭曲可以看作是一个Dirac-Kahler费米子形式。我们发现这种扭曲机制是拓扑场论量子化的一个普适特征，而扭曲的超空间公式隐藏在这个公式背后。N=2的扭曲超空间公式在二维中被制定。4）通过引入二维N=2扭曲超空间的弱不可交换性，在格点上成功地建立了扭曲超空间的形式.现在可以将这个公式应用于格点上N=2的超级杨-米尔斯作用。