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),

本项目1994-1995两个学年的研究成果如下： 1．提出了一种定义 Nambu-Jona-Lasinio (NJL) 模型的新拉格朗日方法，该模型具有由高阶导数费米子动力学项固有的紫外线截止，并保持所有外部规范不变性。我们还讨论了这种高导数系统的量化方法、当前算子和手征异常问题。 2．基于重整化群方法，分析了规范-希格斯-汤川系统是否非平凡；即当紫外线截止值趋于无穷大时，是否能够给出一个明确的相互作用理论。我们证明了它在以下条件下是不平凡的：i）存在渐近自由规范相互作用，其接近渐近自由的速度不应该那么快，ii）汤川耦合应该小于或等于上限，并且iii ）标量四次耦合不是独立参数，而是由 Yukawa 和规范耦合常数唯一确定。在此基础上，证明了规范化NJL模型在四个维度上是可重整化的。 3．阐明了如何从背景场 (BF) 方法中规范不变的有效作用获得物理 S 矩阵的过程。我们给出了一个精确的证明，它给出了与通常的非规范不变（BRS不变）有效作用所获得的相同的S矩阵。 4．我们发现了一个新的关系 1+u=Z_1/Z_3=Z_<顶点>/Z_<波函数>，其中左侧是已知 1+u = 0 给出颜色充分条件的量约束发生，右侧代表重整化因子的比率，Z_<顶点>/Z_<波函数>，它是通用的（即与物质无关），