Grand Unified Theories based on Dynamical Symmetry Breaking

1.提出了定义Nambu-Jona-Lasinio(NJL)模型的一种新的拉格朗日方法，该方法具有高导数费米子动力学项的本征紫外线截止值，并保持了所有的外部规范不变性。我们还讨论了这种高导数系统的量子化方法、电流算符和手征反常问题。基于重整化群方法，分析了规范-Higgs-Yukawa系统是否是非平凡的，即当紫外线截止到无穷大时，它是否能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非平凡的：i)存在一个渐近自由规范相互作用，它的渐近自由度不应该那么快；ii)yukawa耦合小于或等于一个上界；iii)标量四次耦合不是一个独立的参数，而是由yukawa耦合常数和规范耦合常数唯一决定的。在此基础上，证明了规范的NJL模型在四个维度上是可重整化的。阐明了如何从规范不变的背景场有效作用量(BF)方法中得到物理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)有效作用所得到的相同的S矩阵。我们发现了一种新的关系1+u=Z_1/Z_3=Z_&lt；vertex&gt；/Z_&lt；wave-function&gt；，，其中左边是1+u=0已知的量，它给出了色限制发生的充分条件，右边代表重整化因子的比率Z_&lt；vertex&gt；/Z_&lt；波函数&gt；，它是普适的(即，与物质无关的)，

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),