STUDY OF FIELD THEORIES HAVING ULTRA-VIOLET FIXED POINTS

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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.