| SU(2)规范场的恰当形式(欧空间) |
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| 引用本文： | 石赫.SU(2)规范场的恰当形式(欧空间)[J].系统科学与数学,2008,28(7):859-866. |
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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： | 国家重点基础研究发展计划(973计划) |
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| 摘 要： | 应用数学机械化方法研究欧氏空间中SU(2)规范场的正规化问题.首先对Yang-Mills方程的表述进行了讨论,给出了一种具有物理和几何意义的YM-方程,称其为恰当的(exact)YM-方程.对于这种恰当的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.经由示性变换,将非线性的恰当的YM-方程变为一组Laplace方程,实现了SU(2)规范场方程的线性化,即场方程的正规化.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)规范场 恰当的Yang-Mills方程 示性变换 |
| 收稿时间： | 2006-3-28 |
The Exact Yang-Mills Gauge Fields of SU(2) in Euclidean Space |
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| SHI He.The Exact Yang-Mills Gauge Fields of SU(2) in Euclidean Space[J].Journal of Systems Science and Mathematical Sciences,2008,28(7):859-866. |
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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: | The reguralization of SU(2) Yang-Mills gauge fields is presented by using the method of mathematics mechanization in this paper. Two fundamental concepts are introduced: exact Yang-Mills equation and characteristic transformation of Yang-Mills gauge fields. Based on the two concepts, the specializations of SU(2)gauge fields are realized, that is, the linearizations of exact Yang-Millsequations are obtained via characteristic transformations. Thus, the existence of $SU(2)$ Yang-Mills gauge fields is proved. |
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| Keywords: | Mathematics mechanization SU(2) gauge fields special Yang-Millsequations characteristic transformation |
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