STUDY OF FIELD THEORIES HAVING ULTRA-VIOLET FIXED POINTS

就轨距部门而言，特奇变色（TC）是一个非常有吸引力的想法。不幸的是，ETC导致了一场现象学上的灾难，即过度改变味道的中性电流（FCNC）。发现具有非平凡紫外不动点的理论，如果它们确实存在，就可以解决FCNC问题，因为它们的大反常维数会自动提高费米子的动力质量，从而保持了对FCNC的足够抑制。这就是对后一种模式进行认真研究的原因。本课题的目的是研究和分析具有非平凡紫外不动点的理论的结构。我们的主要成果有：(1)利用阶梯Schwinger-Dyson方程。将固定耦合常数的理论与通常的运行耦合常数进行了比较。发现后者不足以抑制FCNC。(2)利用现代重整化技术，明确了阶梯S-D方程解的规范依赖问题；朗道规被发现是一个紫外线固定点。并讨论了渐近自由（AF）和渐近非自由（ANF）规范理论的紫外点结构；我们提出了一个统一处理AF和ANF理论的框架。(3)最近的实验发现顶夸克质量很重。这表明与顶夸克相关的相互作用非常强。在这种情况下，希格斯粒子可能是复合的，并且存在一些临界能量尺度，超过这个尺度，新的物理学就开始了。复合条件与重整化群方程结合在一起，在这类动力系统的表述中起着重要作用。然而，如果使用通常的质量无关重整化群方程，则会导致与复合条件不一致。我们指出，这是由于重希格斯质量的影响，必须使用质量相关的重整化群方程。

Techinicolor(TC) is a very attractive idea so far as the gauge sector is concerned. Unfortunately ETC leads to a phenomenological disaster, the excessive flavor-changing neutral currents (FCNC). The theories having nontrivial ultraviolet fixed point, if they really exist, are found to solve the FCNC problem because of the large anomalous dimension which automatically raised the dynamical fermion masses, preserving the enough suppression of FCNC. This is the reason why the latter model was seriously examined. The purpose of this project is to study and analyze the structure of the theories having a nontrivial ultraviolet fixed point. Our main results are:(1) Using the ladder Schwinger-Dyson equation. comparison is made of the theories with fixed coupling constant with the usual running coupling constant. It is found that the latter is not enough to suppress FCNC.(2) Using the modern renormalization technique we made clear the problems of gauge dependence of the solutions of ladder S-D equation; the Landau gauge ia found to be an ultra-violet fixed point. Also the structure of the ultr-violet points of asymptotically-free (AF) and asymptotically nonfree(ANF) gauge theories; we propose the framework for treating both AF and ANF theories in a unified way.(3) The top quark mass is found to be very heavy from the recent experiments. This indicates that the interaction relevant to top quark is very strong. In such cases Higgs particles may be composite and there are some critical energy scale above which a new physics begin. The compositeness condition, combined with the renormalization group equations, plays an important role in formulating such dynamical system. However if one use the usual mass independent renormalization group equations, we are led to the inconsistency with the compositeness condition. We pointed out that this is because of the effects of the heavy Higgs mass and the mass-dependent renormalization group equation must be used.