General Decomposition Theory of SO(n) Gauge Potential

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

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《中国物理C》（英文）编辑部

2024年10月30日

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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[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.
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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.