A Study on the Complete Integrability of the <i>SU</i>(2) and <i>SU</i>(3) Self-Dual Yang-Mills Source-Free Field Equation System

Li Fubin

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1992, Vol. 16> Issue(S2) : 155-161

A Study on the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equation System

Li Fubin

Department of Mathematics and Mechanics, China University of Mining Technology, Xuzhou, Jiangsu;CCAST(World Laboratory), Beijing, China

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Abstract：
With the theory of harmonic maps and the eight-dimensional Riemannian manifold, the completely integrable SU(2) and SU(3) self-dual Yang-mills source-free field equations are described. Sixteen independent Killing vector fields are determined, two transformation groups which map solutions into solutions are constructed, and conjecture on the complete integrability of systems by the inverse scattering method is formulated.

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[13]	LI Fu-Bin . Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions. Chinese Physics C, 1992, 16(5): 408-413.
[14]	Zheng Xite , Xu Yong . Analytic Study of SU(3) Lattice Gauge Theory. Chinese Physics C, 1989, 13(S3): 249-252.
[15]	XIE Shu-Qin , ZHANG Qi-Ren . AN SU(3) SYMMETRY IN THE TRIBARYON SYSTEM. Chinese Physics C, 1988, 12(5): 673-682.
[16]	Dong Fang-xiao , Zhou Xian-jian , Huang Tao , Xue Pei-you . THE TIME-DEPENDENCES OF THE STATIC SOLUTION OF SU(2) AND SU(3) GAUGE THEORY AT THE PRESENCE OF STATIC EXTENDED SOURCE. Chinese Physics C, 1980, 4(6): 724-734.
[17]	WU YONG-SHI . THE HOLONOMY FUNCTIONAL FORMULATION OF YANG-MILLS FIELD EQUATIONS. Chinese Physics C, 1979, 3(3): 382-386.
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[20]	WU YONG-SHI , CHEN SHIH , TU TUNG-SHENG , GUO HAN-YING . DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU₂ & SO₃ GAUGE FIELD. Chinese Physics C, 1977, 1(1): 52-64.

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Li Fubin. A Study on the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equation System[J]. Chinese Physics C, 1992, 16(S2): 155-161.

Li Fubin. A Study on the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equation System[J]. Chinese Physics C, 1992, 16(S2): 155-161. shu

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Received: 1991-06-05

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Supported by the National Natural Science Foundation of China.

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沈阳化工大学材料科学与工程学院沈阳 110142

A Study on the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equation System

Li Fubin

Department of Mathematics and Mechanics, China University of Mining Technology, Xuzhou, Jiangsu;CCAST(World Laboratory), Beijing, China

Received Date: 1991-06-05

Fund Project: Supported by the National Natural Science Foundation of China.

Abstract: With the theory of harmonic maps and the eight-dimensional Riemannian manifold, the completely integrable SU(2) and SU(3) self-dual Yang-mills source-free field equations are described. Sixteen independent Killing vector fields are determined, two transformation groups which map solutions into solutions are constructed, and conjecture on the complete integrability of systems by the inverse scattering method is formulated.