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.
Abstract
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.
关键词
数学机械化 /
SU(3)规范场 /
恰当的 Yang-Mills 方程 /
示性变换
{{custom_keyword}} /
Key words
mathematics mechanization /
SU(3) gauge fields /
exact Yang-Mills equation /
characteristic transformations
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Chern S. S., Collected Works of Shiing-Shen Chern (in Chinese), East China Normal University Press, Shanghai, 2002.
[2] Shi H., The exact Yang-Mills gauge fields of SU(2) in Euclidean space (in Chinese), Journal of System Science and Mathematical, 2008, 28(7): 859-866.
[3] Shi H., The exact Yang-Mills gauge fields of SU(3) in Euclidean space, Acta Mathematica Sinica, Chinese Series, 2008, 51(5): 833-840.
[4] Shi H., The mathematical formulation of SU(2) gauge fields in Minkowski space, Manuscript.
[5] Shi H., The mathematical formulation of SU(3) gauge Fields in Minkowski space (in Chinese), Frontier Science, 2009, 2(3): 22-28.
[6] Shi H., The geometric analysis of SU(2) gauge fields in Artin space (in Chinese), Manuscript.
[7] Witten E., Quantum Yang-Mills theory (in Chinese), Mathematics, 2001, 2: 100-111.
[8] Wu W. T., Wu Wentsün on Mathematics Mechanization (in Chinese), Shangdong Education Press, Ji'nan, 1996.
[9] Wu W. T., Mathematics Mechanization (in Chinese), Science Press, Beijing, 2002.
[10] Yang C. N., Mills R. L., Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev., 1954, 96(1): 191-195.
[11] Zhang H. Q., Superfluous order and the proper solutions of Maxwell equation, Applied Math. and Mech., 1981, 2(3): 349-360.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
基金
国家重点基础研究发展规划项目(G2004CB318000)
{{custom_fund}}
PDF(512 KB)
