THE U1 GAUGE FIELD IN A SUN GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

GU CHAO-HAO

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1978, Vol. 2> Issue(4) : 295-304

THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

GU CHAO-HAO

Futan Unvivercity

Abstract
HTML
Reference
Related

PDF

Abstract：
Let F be a SU_N gauge field on the space-time manifold M₄, b_λ（x）（λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, f_λμ and Q（x） are SU_N'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M₄' be the set of x such that Q（x）≠0 and define on M₄', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations F_λμ,v+F_μv,λ+F_v_λ,μ=0 are satisfied for arbitrary b_λ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'₄ into the AⅢ type symmetric space SU_N/S(U_s X U_N-s) and the integral is an extension of Kronecker index for N=2.

References

[1]

G. 't Hooft, Nucl. Phys., B79(1974), 276.[2] 侯伯宇、段一士、葛墨林，兰州大学学报(自然科学版)，1975, 2, 26.[3] J. Arafune, P. G. O. Freund and C. J. Goebel, Jour. Math. Phys., 16(1975), 433.[4] T. T. Wu, C. N. Yang, Phys. Rev., D12(1975), 3845;C. N. Yang, "Gauge Fields", (Proc. 1975 Hawaii Conf.).[5] 谷超豪、杨振宁，中国科学，1976, 6, 610; Scientia Sinica, 20 (1977), 177.[6] Z. F. Ezawa and H. C. Tze, Nucl. Phys., B100(1975), 1.[7] W. J. Marciano and H. Pagels, Phys. Rev., D12(1975), 1093.[8] 谷超豪，复旦学报(自然科学版)，1975, 4, 82;中国科学，1976, 3, 320.[9] И. М. Mxanoc, H 3. R., "TIpeArrabneHxA rpyrm BpaiuexHH“rppm}TIopeHUa, , (1958, Mocx日a), 33-34.[10] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press (1962), 354.

[1]	LIAO Ling , HUANG Yong-Chang . Faddeev-Jackiw Quantization of the Gauge Invariant Self-Dual Fields Relative to String Theory. Chinese Physics C, 2006, 30(3): 191-195.
[2]	HUI Ping . Higher Order RPA Calculation of the Glueball Wave Function in 2+1-D SU(2) LGT. Chinese Physics C, 2005, 29(4): 345-349.
[3]	HUI Ping , ZHENG Tai-Yu , WANG Zhou-Fei . Approximated Calculation of the Glueball Mass in the 2+1-D SU(2) LGT with the RPA Method. Chinese Physics C, 2004, 28(6): 580-583.
[4]	HUI Ping . Seventh Order Glueball Mass of the 2+1-D SU(2)LGT in RPA. Chinese Physics C, 2004, 28(11): 1146-1149.
[5]	HUI Ping . Sixth Order Approximation of the Glueball Wave Function in 2+1-DSU(2)LGT. Chinese Physics C, 2000, 24(7): 636-641.
[6]	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.
[7]	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.
[8]	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.
[9]	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.
[10]	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.
[11]	Miao Yangang , Liu Yaoyang . Faddeev-Jackiw Quantitation of a Theory of Self-Dual Fields Interacting with Gauge Fields. Chinese Physics C, 1994, 18(1): 58-61.
[12]	MIAO Yan-Gang . Path Integral Light-Cone Quantization of a Gauge Theory of Self-Dual Fields. Chinese Physics C, 1992, 16(7): 596-599.
[13]	PAN Feng . Vector Coherent State Representations of SU₃ in U₁ U₁ Basis. Chinese Physics C, 1991, 15(1): 80-86.
[14]	YU Yue , GUO Han-Ying . ON GEOMETRIC QUANTIZATION FOR THE BOSONIC STRINGS(1). Chinese Physics C, 1989, 13(5): 419-428.
[15]	JING Si-Cong , RUAN Tu-Nan . ON THE QUANTIZATION OF PURE GAUGE FIELDS ON COSET SPACE OF ABELIAN CHIRAL GROUP. Chinese Physics C, 1988, 12(6): 773-781.
[16]	GUO Shuo-Hong , CHEN Hao . EXACT RESULTS FOR THE TOPOLOGICAL CHARGE OF 1+1D LATTICE GAUGE THEORY. Chinese Physics C, 1987, 11(6): 844-848.
[17]	ZHAO BAO-HENG , YAN MU-LIN . CANONICAL QUANTIZATION OF GAUGE FIELDS(Ⅱ)——SPONTANEOUSLY BROKEN GAUGE FIELDS. Chinese Physics C, 1979, 3(1): 52-59.
[18]	YAN MU-LIN , BAO XI-MING , ZHAO BAO-HENG . CANONICAL QUANTIZATION OF GAUGE FIELDS (Ⅲ)——GRAVITATIONAL FIELD. Chinese Physics C, 1979, 3(5): 582-594.
[19]	ZHAO BAO-HENG , YAN MU-LIN . CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD. Chinese Physics C, 1978, 2(6): 501-510.
[20]	WU YONG-SHI , CHEN SHIH , TU TUNG-SHENG , GUO HAN-YING . DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU₂ & SO₃ GAUGE FIELD. Chinese Physics C, 1977, 1(1): 52-64.

Access

Get Citation

GU CHAO-HAO. THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES[J]. Chinese Physics C, 1978, 2(4): 295-304.

GU CHAO-HAO. THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES[J]. Chinese Physics C, 1978, 2(4): 295-304. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1976-09-07
Revised: 1900-01-01

Article Metric

Article Views(1691)
PDF Downloads(245)
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

THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

GU CHAO-HAO

Futan Unvivercity

Received Date: 1976-09-07
Accepted Date: 1900-01-01
Available Online: 1978-08-05

Abstract: Let F be a SU_N gauge field on the space-time manifold M₄, b_λ（x）（λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, f_λμ and Q（x） are SU_N'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M₄' be the set of x such that Q（x）≠0 and define on M₄', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations F_λμ,v+F_μv,λ+F_v_λ,μ=0 are satisfied for arbitrary b_λ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'₄ into the AⅢ type symmetric space SU_N/S(U_s X U_N-s) and the integral is an extension of Kronecker index for N=2.