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Analytic approach to nonperturbative aspects of gauge theories

规范理论非微扰方面的分析方法

基本信息

批准号：
13135203
负责人：
FUJIWARA Takanori
金额：
$ 4.22万
依托单位：
Ibaraki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13135203/
关键词：
gauge theory lattice gauge theory chiral anomaly effective field theory confinement index theorem topological charge regularization gauge field lattice gauge theory chiral anomaly Dirac operator lattice fermion magnetic monopole

项目摘要

To have better understandings about nonperturbative aspects of guage field theories such as topological structure, constructive formulation, supersymmetry and quark confimenent it is helpful to develop analytical methods such as lattice gauge theory and effective field theory approaches.In lattice gauge theory approach we investigated chiral gauge theories based on lattice Dirac operator satisfying the Ginsparg-Wilson relation and made it clear the topological structure of lattice gauge fields (Fujiwara). Furthermore, we developeded a cohomological method to classify topological invariants. This tourned out to be useful to facilitate construction of chiral U(1) gauge theories on the lattice. Furthermore, we gave a concrete construction of the fermion measure for SU(2)xU(1) electroweak gauge theory on the lattice (Kikukawa). We also investigated lattice regularization of supersymmetric gauge theories and gave a lattice formulation of N=(2, 2) supersymmetric Yang-Mills theory in lower dimensions (Suzuki).The topological structure of abelian gauge theories on a periodic lattice can be understood from abelian gauge theory on a torus. We investigated Dirac operator zero-modes on a torus with a uniform magnetic background in arbitrary even dimensions (Fujiwara). The twisted boundary conditions for the wave functions can be resolved by making use of the geometric nature of the torus. The eigenvalue problem can be solved completely. We found that a set of zero-mode with a desired chirality appear and the degeneracy of the zero-modes can be understood from the magnetic translation symmetry of the background gauge field. Our results are perfectly consistent with the index theorem.In effective field theory approach we investigated Cho-Faddeev-Niemi decomposition of Yang-Mills fields and explained the mechanism of quark confinement by reformulating the theory in terms of the nonlinear field transformations (Kondo).

为了更好地理解规范场论的非微扰方面，如拓扑结构、构造公式、超对称性和夸克约束，有助于发展格子规范理论和有效场论方法等分析方法。在格子规范理论方法中，我们研究了基于满足 Ginsparg-Wilson 关系的格子狄拉克算子的手性规范理论，并明确了规范场理论的拓扑结构。晶格规范场（藤原）。此外，我们开发了一种上同调方法来对拓扑不变量进行分类。事实证明，这对于促进在晶格上构建手性 U(1) 规范理论很有用。此外，我们给出了格子（Kikukawa）上SU(2)xU(1)电弱规范理论的费米子测度的具体构造。我们还研究了超对称规范理论的晶格正则化，并给出了低维 N=(2, 2) 超对称杨-米尔斯理论的格子公式（Suzuki）。周期晶格上的阿贝尔规范理论的拓扑结构可以从环面上的阿贝尔规范理论来理解。我们研究了任意偶数维度上具有均匀磁场背景的圆环上的狄拉克算子零模式（Fujiwara）。波函数的扭曲边界条件可以通过利用环面的几何性质来解决。特征值问题就可以得到彻底解决。我们发现出现了一组具有所需手性的零模，并且可以从背景规范场的磁平移对称性来理解零模的简并性。我们的结果与指数定理完全一致。在有效场论方法中，我们研究了Yang-Mills场的Cho-Faddeev-Niemi分解，并通过用非线性场变换（Kondo）重新表述理论来解释夸克禁闭机制。