Grand Unified Theories based on Dynamical Symmetry Breaking

基于动力学对称性破缺的大统一理论

基本信息

批准号：
06640387
负责人：
KUGO Taichi
金额：
$ 1.54万
依托单位：
KYOTO 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：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

The research results of our project for two academic years in 1994-1995 are as follows :1. A new lagrangian way of defining the Nambu-Jona-Lasinio (NJL) model is proposed, which possesses an intrinsic ultraviolet cutoff by the higher derivative fermion kinetic term and maintains all the external gauge invariances. There we also discussed the quantization method of such a higher-derivative system, current operators and chiral anomaly problems.2. Based on the renormalization group method, the gauge-Higgs-Yukawa system was analyzed whether it is nontrivial or not ; namely, whether it can give a well-defined interacting theory when the ultraviolet cutoff goes to infinity. We proved that it is nontrivial under the following conditions : i) there exists an asymptotically free gauge interaction, whose approach to the asymptotic freedom should not be so rapid, ii) the Yukawa coupling should be smaller than or equal to an upperbound, and iii) the scalar quartic coupling is not an independent parameter but is uniquely determined by the Yukawa and gauge coupling constants. Based on the result, the gauged NJL model is proved to be renormalizable in four dimensions.3. The procedure was clarified how one can obtain the physical S-matrix from the gauge-invariant effective action in the background field (BF) method. We gave a precise proof that it gives the same S-matrix as the one obtained by the usual non-gauge-invariant (BRS invariant) effective action.4. We found a new relation 1+u=Z_1/Z_3=Z_<vertex>/Z_<wave-function>, where the left-hand side is the quantuty that 1+u = 0 is known to give a sufficient condition for the color confinement to occur, and the righthand side stands for the ratio of the renormalization factors, Z_<vertex>/Z_<wave-function>, which is universal (i.e., matter-independent),

我们在1994 - 1995年的两个学年的项目的研究结果如下：1。提出了一种定义Nambu-Jona-Lasinio（NJL）模型的新的Lagrangian方法，该模型提出了较高的衍生效率动力学项，并具有固有的紫外线截止，并维持所有外部仪表的不向导。在那里，我们还讨论了这种高衍生系统，当前操作员和手性异常问题的量化方法。2。基于重新归一化的组方法，分析了量规 - 宽川系统是否非平凡。也就是说，当紫外线临界值进入无限时，它是否可以提供明确的相互作用理论。我们证明了在以下条件下这是非平凡的：i）存在渐近的自由量规交互，其对渐近自由的方法不应那么快，ii）ii）Yukawa耦合应小于或等于上的或等于上的覆盖物，而III）coupling Quartic Quartic Quartic coupling并不是独立的参数，而是由无孔确定的Yukawa and yukaua。基于结果，证明了测量的NJL模型在四个维度上是可重新分配的。3。阐明了该过程如何从背景字段（BF）方法中的量规不变有效作用中获得物理S-矩阵。我们给出了一个确切的证据，表明它给出了与通常的非规范不变（BRS不变）有效动作相同的S-Matrix。4。我们找到了一个新的关系1+u = z_1/z_3 = z__ <vertex>/z__ <wave-function>，其中左侧是1+u = 0的量子，可以给出足够的条件，可以使颜色限制出现，而righthand的侧面是rentrate sand in e renormization因子的比例，z___________________/z_ <vertex>/z_ <wave。独立于物质），