| Yang-Mills规范场的存在性、可解性(一) |
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| 引用本文： | 石赫.Yang-Mills规范场的存在性、可解性(一)[J].系统科学与数学,2009,29(9):1200-1210. |
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| 作者姓名： | 石赫 |
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| 作者单位： | 中国科学院数学与系统科学研究院数学机械化重点实验室,北京,100190 |
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| 基金项目： | 国家基础研究发展规划项目(G2004CB318000)资助课题 |
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| 摘 要： | 应用数学机械化方法研究欧氏空间中$SU(2)$ Yang-Mills规范场的存在性问题.首先对YM--方程的结构进行了讨论,说明YM--方程由它的奇部份和偶部份联立组成.对于YM--方程构造了一类线性微分变换,称之为$SU(2)$规范场的示性变换.经示性变换,将非线性的YM--方程的奇部份变为一组Laplace方程,实现了$SU(2)$规范场方程的线性化.从而证明了$SU(2)$规范场存在3个独立的Yang-Mills规范场.
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| 关 键 词： | 数学机械化 SU(2)Yang-Mills 规范场 示性变换. |
| 收稿时间： | 2009-6-10 |
| 修稿时间： | 2009-6-28 |
EXISTENCE AND SOLVABILITY OF YANG-MILLS GAUGE FIELDS OF SU(2)IN ESULIDEAN SPACE |
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| SHI He.EXISTENCE AND SOLVABILITY OF YANG-MILLS GAUGE FIELDS OF SU(2)IN ESULIDEAN SPACE[J].Journal of Systems Science and Mathematical Sciences,2009,29(9):1200-1210. |
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| Authors: | SHI He |
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| Institution: | Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 |
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| Abstract: | Existence and solvability of Yang-Mills gauge fields of SU(2) in Euclidean space is studed in this paper. The existence of Yang-Mills gauge fields is proved andthe solvability of Yang-Mills equation is presented using the method ofMathematics Mechanization. The fundamental concepts of characteristictransformations of Yang-Mills gauge fields are introduced. The linearizations of Yang-Mills equations are obtained via characteristic transformations. |
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| Keywords: | Mathematics mechanization Yang-Mills gauge fields of SU(2) characteristic transformation |
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