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

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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

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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.