Artin空间中SU(3)规范场的几何解析

The Geometric Analysis of SU(3) Gauge Fields in Artin Space

研究4维Artin空间中SU(3)规范场的线性化问题.首先对Yang-Mills方程的推导进行了讨论,给出了恰当的Yang-Mills方程的概念,其具有明确的几何意义.其次,构造了一类线性微分变换,称之为Artin空间SU(3)规范场的示性变换.示性变换是应用数学机械化方法确定的.经由示性变换,将非线性的恰当的Yang-Mills方程变为一组线性方程,实现了SU(3)规范场的场方程的线性化.从而证明了,对于恰当的Yang-Mills方程,SU(3)规范场包括8个独立的规范场.

This paper aims to study the linearizations of SU（3） Yang-Mills gauge fields in Artin space which is 4-dimensional.First,the Yang-Mills equation is discussed, and the concept of exact Yang-Mills equation is given,and it has explicit geometric meanings.Then a kind of differential transformation,which is called characteristic transformation of SU（3） Yang-Mills gauge fields in Artin space,is constructed.The characteristic transformation is obtained by the method of mathematics mechanization .The linearizations of exact Yang-Mills equations are obtained via characteristic transformations.Thus,the existence of SU（3） Yang-Mills gauge fields is proved.