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Investigations of anomalies and the undex theorem in lattice chiral gauge theories based on noncommutative differential geomerty

基于非交换微分几何的格子手征规范理论中的反常现象及UNDEX定理研究

基本信息

批准号：
13640258
负责人：
FUJIWARA Takanori
金额：
$ 2.11万
依托单位：
Ibaraki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (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

项目摘要

Based on the Dirac operator satisfying the Ginsparg-Wilson relation, we have investigated the topological structures of lattice chiral gauge theories and their roles in quantum theory The configuration space of any lattice fields cannot have nontrivial topological structure since any field configurations can be continuously deformed into the trivial one. By restricting the configurations by imposing a kind of smoothness condition it is possible to introduce topologically nontrivial structures. In the case of gauge fields the effects of such nontrivial topological structures can be proved by coupling chiral lattice fermions.In vector-type massless gauge theories like QCD we can formulate chirally symmetric lattice action in terms of the overlap Dirac operator. In this case the fermion measure cannot be chirally symmetric but yields chiral anomaly in the form of Jacobian. The overlap Dirac operator is not well-defined over the entire configuration space of the lattice gauge fields but is … More defined only for smooth configurations. This implies that the configuration space of the lattice fields where the theory is well-defined is disconnected into several connected components. We have numerically analyzed the spectral flows of hermitian Wilson-Dirac operator for abelian gauge backgrounds and shown that the index of the lattice Dirac operator changes in accord with the change of the topological charge for gauge field that can be considered smooth. We have also established the chiral anomaly in the classical continuum limit for the nonabelian gauge backgrounds in arbitrary even dimensions by evaluating the Jacobian of the fermion measure under the chiral transformations.The smoothness condition may also introduces notrivial topological structure like a hole in a connected component. We have investigated the effects of such topological structure by coupling chiral fermions and have succeeded in constructing the Wess-Zumino-Witten action. By doing this we have established the existence of nontrivial. topological structure even in a connected component that is related with the gauge anomalies. Less

基于满足Ginsparg-Wilson关系的Dirac算符，我们研究了格点手征规范场的拓扑结构及其在量子理论中的作用。任何格点场的位形空间都不可能具有非平凡的拓扑结构，因为任何场的位形都可以连续地变形为平凡的。通过施加一种光滑条件来限制组态，就有可能引入拓扑非平凡结构。在规范场的情况下，这种非平凡拓扑结构的效应可以通过耦合手征格点费米子来证明，在矢量型无质量规范场理论如QCD中，我们可以用重叠Dirac算符来表示手征对称格点作用量。在这种情况下，费米子测度不能是手征对称的，但会产生雅可比矩阵形式的手征反常。重叠狄拉克算子在格点规范场的整个位形空间上并没有很好的定义，但 ...更多信息仅为平滑配置定义。这意味着格场的位形空间在理论定义良好的地方是不连接成几个连通分量的。数值分析了阿贝尔规范场背景下厄米Wilson-Dirac算符的谱流，证明了格点Dirac算符的指数随规范场拓扑荷的变化而变化，这种变化雅阁。通过计算费米子测度在手征变换下的雅可比矩阵，我们还建立了任意偶数维非交换规范背景在经典连续极限中的手征反常，光滑条件也可以引入连通分量中的空穴等非平凡拓扑结构.我们通过耦合手征费米子研究了这种拓扑结构的影响，并成功地构造了Wess-Zumino-维滕作用量。通过这样做，我们已经建立了非平凡的存在性。拓扑结构，甚至在一个连接的组件，是有关的规范异常。少