Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions

LI Fu-Bin

Chinese Physics C> 1992, Vol. 16> Issue(5) : 408-413

Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions

LI Fu-Bin ^,

The Mathematical-Mechanical Department,China University of Mining Technology,Xuzhou 221008

Abstract
HTML
Reference
Related

PDF

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 a conjecture on the complete integrability of systems by the inverse scattering method is formulated.

References

[1]

B. C., Xanthopoulous, J. Phys. A14(1981), 1445.[2] L. R. Eisenhart, Riemannian Gecmetry; Princeton, NJ, Princeton University Press, 1926[3] P. D. Lax, Commun. Pure. Appl. Math., 21(1968), 467.[4] A. C. Scott, E. Y. F. Chu, D. W. Melaughlin, Proc. IEEE., 61(1973), 1443.[5] P, Summers, PhD, thesis, the University of Texas at Austin, 1973.[6] F. Ernst, Phys. Rev., 167(1968), 1175.[7] D. Maison, Phys. Rev, Lett 41(1978), 521.[8] D. Maison, J. Math. Phys., 25(1979), 871.[9] B. K. Harrison, Phys, Rev. Lett., 41(1978), 1197.[10] V. A. Belinskii, V. E. Xakharov, Sov, Phys.JETP, 48(1978), 985.[11] V, A. Belinskii, V. E. Zakharov, Sov. Phys. JETP, 50(1979), 1.[12] R. A. Matzner, C. W. Misner, Phys. Rev., 154(1976), 1229.[13] F. Ernst, Phys. Rev., 168(1968), 1415.[14] G. A. Alekseyev, Proc. GrG, vol. 11(1980), 231,[15] C. Hoenselaers, J. Math, Phys., 19(1978), 539.[16] D, Kramer, Stephani H, Mac Callum M, HerIt E, Exact Solutions of Einstein's Field Equations, Cambridge: Cup, 1980.[17] W. Kinnersley, J. Math; Phys., 14(1973), 651[18] S. V, Manakov, V, E. Zakharov, Lett. Math, Phys., 5(1981), 247.[19] V. E. Zakharov, A. V. Mikhailov, Sov. Phys. -JETP, 47(1978), 1017.

[1]	Andrea Addazi , Pietro Donà , Antonino Marcianò . Dynamical interactions of dark energy and dark matter: Yang-Mills condensate and QCD axions. Chinese Physics C, 2018, 42(7): 075102. doi: 10.1088/1674-1137/42/7/075102
[2]	Yacine Bouguerra , Mustapha Maamache , Jeong Ryeol Choi . Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay's angle. Chinese Physics C, 2017, 41(6): 065103. doi: 10.1088/1674-1137/41/6/065103
[3]	Jong-Ping Hsu . Quark confinement, new cosmic expansion and general Yang-Mills symmetry. Chinese Physics C, 2017, 41(1): 015101. doi: 10.1088/1674-1137/41/1/015101
[4]	. Addendum: Quark Confinement, New Cosmic Expansion and General Yang-Mills Symmetry. Chinese Physics C, 2017, 41(12): 129102.
[5]	HSU Jong-Ping . A model of uni ed quantum chromodynamics and Yang-Mills gravity. Chinese Physics C, 2012, 36(5): 403-409. doi: 10.1088/1674-1137/36/5/005
[6]	WANG Dian-Fu , SUN Xiao-Yu , CHANG Xiao-Jing . Dynamical CP violation of the generalized Yang-Mills model. Chinese Physics C, 2011, 35(2): 130-134. doi: 10.1088/1674-1137/35/2/004
[7]	HUI Ping , CHEN QiZhou . 0⁺⁺ Glueball Mass in 2+1-D SU(3) LGT. Chinese Physics C, 2000, 24(9): 805-809.
[8]	Hul Ping . (2+1)-D SU(3)0⁺⁺ Glueball Wavefunction. Chinese Physics C, 1999, 23(4): 340-346.
[9]	Liu Yaoyang , Sun Lazhen , Jiang Xiangdong . SU(3)_C×SU(2)_I×U(1)_Y Theory of Composite Leptons. Chinese Physics C, 1998, 22(11): 996-1003.
[10]	Chen Qizhou , Fang Xiyan , Guo Shouhong . Calculation of Vacuum State for 2+1-Dimensional SU(3) Lattice Gauge Theory. Chinese Physics C, 1995, 19(5): 398-404.
[11]	Zhao Liu . Hamiltonian Reductions of Supersymmetric Self-Dual Yang-Mills Model. Chinese Physics C, 1993, 17(S4): 361-369.
[12]	Zhao Liu . Supersymmetrization of Self-Dual Yang-Mills Theory. Chinese Physics C, 1993, 17(S4): 347-353.
[13]	Li Fubin . A Study on the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equation System. Chinese Physics C, 1992, 16(S2): 155-161.
[14]	CHEN Tian-Lun , SUO Cun-Chuan , HUANG Wu-Qun . β FUNCTION FOR SU(3)×SU(3) CHIRAL MODEL ON 2-DIMENSIONAL RANDOM TRIANGLE LATTICE. Chinese Physics C, 1990, 14(8): 700-703.
[15]	LI ZI-PING . LAGRANGIAN MULTIPLIER AND MASSIVE YANG-MILLS FIELDS YANG-MILLS FIELDS. Chinese Physics C, 1982, 6(5): 555-559.
[16]	MA ZHONG-QI , DONG FANG-XIAO , ZHOU XIAN-JIAN , XUE PEI-YOU . CLASSICAL STATIC AND SPHERICALLY SYMMETRIC SOLUTION OF SU(3) GAUGE FIELD WITH A STATIC AND ECTERNAL EXTERNAL SOURCE. Chinese Physics C, 1981, 5(2): 182-191.
[17]	Tao Fu-zhen , Yao Qi-yuan , Ou Zhi , He Zhi-qiang . THE SPHERICAL SOLUTIONS OF THE SCALAR FIELD EQUATION IN SU (2) GAUGE FIELD THEORY. Chinese Physics C, 1980, 4(2): 179-185.
[18]	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.
[19]	WU YONG-SHI . THE HOLONOMY FUNCTIONAL FORMULATION OF YANG-MILLS FIELD EQUATIONS. Chinese Physics C, 1979, 3(3): 382-386.
[20]	WU YONG-SHI , LEE HWA-CHUNG , KUO SHUO-HUNG , HSEEN TING-CHANG . ON A PSEUDO-PARTICLE SOLUTION OF THE YANG-MILLS FIELD. Chinese Physics C, 1978, 2(4): 371-373.

Access

Get Citation

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[J]. Chinese Physics C, 1992, 16(5): 408-413.

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(2606)
PDF Downloads(422)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Description of the Complete Integrability of the SU(2) and SU(3) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions

LI Fu-Bin ^,

Corresponding author: LI Fu-Bin,

The Mathematical-Mechanical Department,China University of Mining Technology,Xuzhou 221008

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1992-05-05

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 a conjecture on the complete integrability of systems by the inverse scattering method is formulated.