DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU2 &amp; SO3 GAUGE FIELD

WU YONG-SHI; CHEN SHIH; TU TUNG-SHENG; GUO HAN-YING

Chinese Physics C> 1977, Vol. 1> Issue(1) : 52-64

DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU₂ & SO₃ GAUGE FIELD

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper,we discuss magnetic monopo]es of an U1-subgroup in SU2 and SO3 broken gauge theories,on the basis of fibre-bundle theory.We derive a general ex- pression for the electromagnetic potentials around magnetic monopoles,which,accord- ing to the usual connection between the electromagnetic potentials and field-strength tensors,leads naturally to't Hooft's definition of the electromagnetic field-strength tensors.Furthermore,from the view-point of fibre-bundle theory,we elucidate some problems concerning which there exist different opinions in the present literature. Our conclusions are summarized as follows. 1)In general,the description of magnetic monopoles in SU2 and SO3 broken gauge theories needs,in addition to SU2 or SO3 gauge potentials,the introduction of an unimodular Higgs isovector field to specify the direction of charge in the isospin space. 2)For the existence of magnetic monopoles,it is only required that the corresponding principal SU2-or SO3-bundles be reduced to U1-or SO2-bundles,not that the corresponding SU2-or SO3-gauge potentials be also reduced to U1-or SO2-gauge potentials. 3)The usual conclusion that the values of magnetic monopoles depend only on the topological properties of the Higgs field holds for the product SU2-or SO3-bundle. For the nontrivial SO3-bundle a new detailed discussion is needed.

References

[1]

G. t'Hooft, Nzcel. Plays., B79 (1974), 276.[2] A. M. Po1yakov, J. E. T. P., (1974).[3] 侯伯宇，段一士，葛墨林，兰州大学学报，2 (1975), 26. 物理学报，25 (1976), 514. 段一士，葛墨林，科学通报，21 (1976), 382.[4] 李华锤，冼鼎昌，郭硕鸿，中山大学学报，3 (1975) 7; 物理学报，25 (1976), 507.[5] J. Arafune, P. G. O. Freund C. J. Goebel, Jourl. math. Phys.,16(1975), 433.

[1]	JIANG Jun-Qin . Vector Meson Masses in Two-dimensional SU(NC) Lattice Gauge Theory with Massive Quarks. Chinese Physics C, 2008, 32(1): 9-12. doi: 10.1088/1674-1137/32/1/002
[2]	JIANG Jun-Qin . Quark Condensate in Two-Dimensional SU(N_C) Lattice Gauge Theory with Massive Wilson Quarks. Chinese Physics C, 2007, 31(1): 19-22.
[3]	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.
[4]	JIANG JunQin . Study of the Vacuum State for 2+1 Dimensional SU(2) Lattice Gauge Field Theory. Chinese Physics C, 2000, 24(10): 922-926.
[5]	Hui Ping , Cai Pengfei , Chen Qizhou . Analytic calculation of Glueball Mass In (2+1)-D SU(2)Lattice Gauge Theory. Chinese Physics C, 1996, 20(1): 55-60.
[6]	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.
[7]	Chen Qizhou , Li Lei , Li Zhibing , Guo Shuohong . Vacuum Wave Function Study of 2+1 Dimensional SU(2) Gauge Field. Chinese Physics C, 1994, 18(5): 417-423.
[8]	Chen Qizhou , Li Zhibing , Li Lei , Guo Shuohong . Infrared Vacuum Wavefunction of (2+1)-Dimensional SU(2) Gauge Field. Chinese Physics C, 1994, 18(1): 37-42.
[9]	LIU Jin-Ming , GONG Di . Variational Study of 3-Dimensional SU(2) Lattice Gauge Theory with Independent Plaquette Trial Action. Chinese Physics C, 1993, 17(2): 128-133.
[10]	ZHENG Xi-Te , XU Yong . ANALYTIC STUDY OF su(3) LATTICE GAUGE THEORY. Chinese Physics C, 1989, 13(8): 765-768.
[11]	ZHENG Wei-Hong , LIU Jin-Ming , GUO Shuo-Hong . THE MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY. Chinese Physics C, 1988, 12(1): 134-136.
[12]	LIU Jin-Ming , ZHENG Wei-Hong , GUO Shuo-Hong . THE MASS GAP IN 2+1 DIMENSIONAL SU(3) LATTICE CAUGE THEORY. Chinese Physics C, 1988, 12(3): 420-424.
[13]	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.
[14]	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.
[15]	Ge Mo-lin , Duan Yi-shi . SPACE OF CONSTANT CURVATURE AND SU₂-DUAL CHARGES. Chinese Physics C, 1980, 4(2): 173-178.
[16]	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.
[17]	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.
[18]	Ge Mo-lin , Duan Yi-shi . ON THE GAUGE VACUUM EFFECTS IN SU₂ GAUGE THEORY. Chinese Physics C, 1980, 4(5): 539-544.
[19]	HOU BO-YU , HOU BO-YUAN . STATICAL SPHEROSYMMETRICAL SOURCELESS SOLUTION OF SU(2) GAUGE FIELD——THE SELFDUALITY,UNIQUENESS AND THE SELF INDUCED CHARGE CURRENT. Chinese Physics C, 1979, 3(3): 225-265.
[20]	WANG KE-LIN , HSIEN TING-CHANG , CHENG HSI-THE . ON THE MAGNETIC MONOPOLE AND DIPOLE SOLUTION OF THE SU(N) GAUGE FIELD THEORY IN A CURVED SPACE. Chinese Physics C, 1978, 2(3): 275-279.

Access

Get Citation

WU YONG-SHI, CHEN SHIH, TU TUNG-SHENG and GUO HAN-YING. DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU₂ & SO₃ GAUGE FIELD[J]. Chinese Physics C, 1977, 1(1): 52-64.

WU YONG-SHI, CHEN SHIH, TU TUNG-SHENG and GUO HAN-YING. DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU₂ & SO₃ GAUGE FIELD[J]. Chinese Physics C, 1977, 1(1): 52-64. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1977-04-07
Revised: 1900-01-01

Article Metric

Article Views(1846)
PDF Downloads(334)
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

DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU₂ & SO₃ GAUGE FIELD

Received Date: 1977-04-07
Accepted Date: 1900-01-01
Available Online: 1977-11-05

Abstract: In this paper,we discuss magnetic monopo]es of an U1-subgroup in SU2 and SO3 broken gauge theories,on the basis of fibre-bundle theory.We derive a general ex- pression for the electromagnetic potentials around magnetic monopoles,which,accord- ing to the usual connection between the electromagnetic potentials and field-strength tensors,leads naturally to't Hooft's definition of the electromagnetic field-strength tensors.Furthermore,from the view-point of fibre-bundle theory,we elucidate some problems concerning which there exist different opinions in the present literature. Our conclusions are summarized as follows. 1)In general,the description of magnetic monopoles in SU2 and SO3 broken gauge theories needs,in addition to SU2 or SO3 gauge potentials,the introduction of an unimodular Higgs isovector field to specify the direction of charge in the isospin space. 2)For the existence of magnetic monopoles,it is only required that the corresponding principal SU2-or SO3-bundles be reduced to U1-or SO2-bundles,not that the corresponding SU2-or SO3-gauge potentials be also reduced to U1-or SO2-gauge potentials. 3)The usual conclusion that the values of magnetic monopoles depend only on the topological properties of the Higgs field holds for the product SU2-or SO3-bundle. For the nontrivial SO3-bundle a new detailed discussion is needed.