General Decomposition Theory of SO(n) Gauge Potential

LI Xi-Guo; DUAN Yi-Shi; SONG Jian-Jun

Chinese Physics C> 2001, Vol. 25> Issue(4) : 296-303

General Decomposition Theory of SO(n) Gauge Potential

Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Collisions, Lanzhou 730000, China2 Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China3 Institute of Theoritical Physics, Lanzhou University. Lanzhou 730000, China

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Abstract：
By means of devices of geometry algebra the general decomposition of gauge potential (spin connection) on a compact n-dimension Riemannian manifold has been studied in detail. A general decomposition formula of SO(n) gauge potential in terms of a unit vector field on the sphere bundle has been established. Using same local structure between SO(2) and U(1), SO(3) and SU(2) the general decomposition formula of U(1) and SU(2) gauge potential in terms of the unit vector field has been also given respectively.

References

[1]

DUAN Yi-Shi, GE M L. Sci. Sinica, 1979, 11:9; DUAN Yi-Shi. ZHAO S C. Cmmun. Theor. Phys., 1983,2:15532 Witten E. Mompoles and Four-Manifolds, hep-th/94111023 DUAN Y S. SLAC-PUB3301/844 DUAN Y S, ZHANC; S L. Int. J. Eng. Sci. , 1990, 28:689; 1991, 29:1535 LlUAU Y S, MENGMH. J. Math. Phys.. 1993,34:11496 DUAN Y S. LI Xi-Gw. Helv. Phys. Acta, 1995. 68:97 DUAN Y S et al. J. Math. Phys. , 1994. 35:9: LI Xi-Guo. High Energy and Nuclear Physics, 1999. 23(9):906-913(in Chinese)(李希国. 高能物理与核物理,1999, 23(9):906-913)8 Faddeev L, Niemi Antti J. Phys. Rev. Lett., 1999,82(8):16249 Heagemen F E. Johnson K. Nucl. Phys., 1995, B439:59710 Fomenko A T. Differential Geornetiy and Topokgy. New York: Consutants Bureau Press, 198711 Bott R, WU L W. Differential form in Algebratic Topolody. Springes-Verlag Press, 198212 Hestones D, Sobayk G. Clifford Algebra to Geometric Calculus Reidel, Dorelrecht 198413 Doran C, Hestenes D et al. J. Math. Phys., 1993, 34: 3642; Lasenbly, Doran C et al. J . Math. Phys. , 1993, 34:368314 Chem S S. An. da Acad. Brusileira de Ciencias, 1963. 35 : 1715 Eguchi T, Gilueg P B, Hanson A J. Phys. Rep. , 1980,66 :21316 LI Xi-Guo, Doctoral Dissertation. Lanzhou University, 199417 Chem S S. Ann. Math. 1944. 45 : 747; 1945.46 :67418 Kimyeong L et al. Phys, Rev. Lett., 1992, 68: 1100

[1]	LI Xi-Guo , JIA Duo-Jie , GAO Yuan . Decomposition of the SU(2) Gauge Field and Circulation Condition of the Bose-Einstein Condensate. Chinese Physics C, 2003, 27(1): 12-14.
[2]	Gao Haixiao , Li Ziping . Quantal Conserved Charges in Gauge Theory. Chinese Physics C, 1997, 21(6): 506-512.
[3]	Wang Shunjin , Guo Hua . Constrained Correlation Dynamics of SU(N) Gauge Theories in Canonical Form (Ⅱ) Gauge Constrained Conditions. Chinese Physics C, 1995, 19(4): 332-339.
[4]	Yan Xiunling , Jiang Zhijin , Li Zuohong . Quantitative Analysis for U(1) Gauge Theory. Chinese Physics C, 1995, 19(6): 527-533.
[5]	QIU Zhi-Hong , CHEN Chi-Qing , WANG Yan-Sen , CHEN Jian-Xin , HUANG Fa-Yang . THE EFFECTIVE SEPARABLE POTENTIALS BETWEEN n AND α INTERACTIONS. Chinese Physics C, 1993, 17(9): 845-850.
[6]	LUO Xiang-Qian , CHEN Qi-Zhou . Fermion Condensates in Lower Dimensional Gauge Theories. Chinese Physics C, 1992, 16(8): 685-695.
[7]	YAN Xun-Ling . Corrected MK Transformation of Z_N Gauge Theory. Chinese Physics C, 1992, 16(6): 499-504.
[8]	LU Jian-Xin , RUAN Tu-Nan . GAUGE TRANSFORMATION IN STRING THEORY. Chinese Physics C, 1989, 13(4): 309-315.
[9]	XU Zai-Xin . IMPROVED MIGDAL-KADANOFF TRANSFORMATION FOR Z_N LATTICE GAUGE THEORIES. Chinese Physics C, 1988, 12(2): 169-177.
[10]	WANG Qin-Mou . THERMODYNAMICAL PROPERTIES OF GAUGE THEORIES AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL (Ⅱ). Chinese Physics C, 1987, 11(2): 182-185.
[11]	CHEN Hao , GUO Shuo-Hong . ADLER-BELL-JACKIW ANOMALY IN LATTICE GAUGE THEORY. Chinese Physics C, 1986, 10(6): 666-676.
[12]	CHEN De-Fang , SONG Yong-Shen , CHEN Tian-Lun , ZHENG Xi-Te , HE Xiang-Hao , XIAN Ding-Chang . ON THE ANALYTICAL STUDY IN LATTICE GAUGE FIELD THEORY. Chinese Physics C, 1986, 10(1): 32-39.
[13]	WANG Qin-Mou . THERMODYNAMICAL PROPERTIES OF GAUGE THEORIES AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL. Chinese Physics C, 1986, 10(1): 24-31.
[14]	CHEN Tian-Lun , Zhou Hong-Mo , LI Tie-Zong , XIAN Ding-Chang , ZHENG Xi-Te . VARIATIONAL ANALYSIS OF THE SU(3) LATTICE GAUGE THEORY. Chinese Physics C, 1984, 8(5): 653-656.
[15]	HOU Bo-Yu , SHI Kang-Jie , WANG Yu-Bin , HOU Bo-Yuan , WANG Pei . THE NON-SELFDUAL SOLUTIONS OF CP(n) CHIRAL THEORY AND CORRESPONDING GAUGE FIELDS. Chinese Physics C, 1983, 7(2): 150-159.
[16]	Ge Mo-lin , Duan Yi-shi . ON THE GAUGE VACUUM EFFECTS IN SU₂ GAUGE THEORY. Chinese Physics C, 1980, 4(5): 539-544.
[17]	WANG PEI , HOU BO-YU . THE MULTISYNCHRO-SPHERICAL SOLUTIONS OF THE SU(N)GAUGE THEORY. Chinese Physics C, 1979, 3(5): 555-571.
[18]	HOU BO-YU . NONEQUIVALENT SU(2) GAUGE POTENTIALS UNDER EQUAL FIELD STRENTHS AND SOURCES. Chinese Physics C, 1978, 2(1): 61-66.
[19]	GU CHAO-HAO . THE LOOP PHASE-FACTOR APPROACH TO GAUGE FIELDS. Chinese Physics C, 1978, 2(2): 97-108.
[20]	TUAN I-SHIH , KEH MO-LIN . GEOMETRICAL DESCRIPTION OF DECOMPOSIBILITY OF A NON-ABELIAN GAUGE POTENTIAL. Chinese Physics C, 1978, 2(6): 511-514.

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LI Xi-Guo, DUAN Yi-Shi and SONG Jian-Jun. General Decomposition Theory of SO(n) Gauge Potential[J]. Chinese Physics C, 2001, 25(4): 296-303.

LI Xi-Guo, DUAN Yi-Shi and SONG Jian-Jun. General Decomposition Theory of SO(n) Gauge Potential[J]. Chinese Physics C, 2001, 25(4): 296-303. shu

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Received: 2000-05-19
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

General Decomposition Theory of SO(n) Gauge Potential

Corresponding author: LI Xi-Guo,

Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Collisions, Lanzhou 730000, China2 Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 730000, China3 Institute of Theoritical Physics, Lanzhou University. Lanzhou 730000, China

Received Date: 2000-05-19
Accepted Date: 1900-01-01
Available Online: 2001-04-05

Abstract: By means of devices of geometry algebra the general decomposition of gauge potential (spin connection) on a compact n-dimension Riemannian manifold has been studied in detail. A general decomposition formula of SO(n) gauge potential in terms of a unit vector field on the sphere bundle has been established. Using same local structure between SO(2) and U(1), SO(3) and SU(2) the general decomposition formula of U(1) and SU(2) gauge potential in terms of the unit vector field has been also given respectively.