ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

Sun Hung-zhou

Chinese Physics C> 1980, Vol. 4> Issue(1) : 73-92

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

Sun Hung-zhou

Peking University

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper, we analyse the commutation relations of the infintesimal opera-tors of the group SU₃ and find that the eight infinitesimal operators of the groupSU₃ can be written as a scalar operator A, three angular momentum operators (L₁,L_o, L_-1,)and two sets of the irreducible tensor operators of rank 1/2, （T_{±1/2，V_±1/2}）By means of the commutation relations of these operators, all irreducible represen-tations of the group SU₃ can be easily obtained. In this pape, the matrices corresponding to these operators in the irreduciblerepresentation（λμ）, are given; therefore the irreducible representation and its re-presentation space R^λμ are completely defined. Besides, a method for calculatingthe scalar factors of the reduction coefficients and the symmetric relations of thosefactors are also given. As examples, the scalar factors of the reduction coefficientsof （λμ）×（10）, （λμ）×（01）, （λμ）×（20） and （λμ）×（11） are calculated. In the last part of this paper, we define the irreducible tensor operators ofthe group SU₃ and prove the corresponding Wigner-Eckart theory. The method used in the discussion of the group SU₃ be extended to allof the compact simple Lie groups of rank 2 and we shall discuss them in two suc-ceeding papers.

References

[1]

G. Racah, Group Theory and Spectroscopy, Princeton,(1951).[2] R. E. Bchrends et al., Rev. Mod. Phys., 34 (1962),1.[3] A. Salam, Theoretical Physics, p. 173., Viena,(1963).[4] J. P. Elliott et al., Proc. Roy. Soc., A277 (1963), 557.[5] A. Arima et al., Nucl. Phys., A138 (1969),273., A162(1971),605.[6] K. T. Hecht, Nucl. Phys., 63 (1965), 177.[7] G. Gneuss et al., Nucl. Phys., A171 (1971),449.[8] B. H. Flowers et al., Proc. Phys. Soc., 84 (1964),139.[9] A. R. Edmonds, Angular Momentum in Quantum Mechanics, Priceton,(1957).[10] 孙洪洲等,物理学报21(1965), 56,[11] 杨国祯等,北京大学学报(自然科学版)10(1964), 269.[12] S. McDonald et al., J. Math. Phys.,14 (1973),1248.[13] J. P. Draayer et al., J. Math. Phys.,14 (1973),1904.[14] E. M. Haacke et al., J. Math. Phys.,17 (1976),2040.[15] 侯伯宇,中国科学,14(1965), 367.[16] J. J. De Swaat, Rev. Mod. Phys., 35(1963),916.[17] L. C. Biedenharn et a1, J. Math. Phys., 4(1963),1449.,4(1964),1723.,4 (1964),1730.[18] 陈金全等,高能物理与核物理,3(1979),216.

[1]	ZHANG Jian-Bo , TANG Ling-Yun , ZHANG Jiang , QIN Zhen-Xing , ZENG Xiao-Jing , LIU Jing , WEN Jin-Sheng , XU Zhi-Jun , GU Genda , CHEN Xiao-Jia . Pressure-induced isostructural phase transition in Bi₂Sr₂CaCu₂O_8+δ. Chinese Physics C, 2013, 37(8): 088003. doi: 10.1088/1674-1137/37/8/088003
[2]	M. Ablikim et al (BESⅡ collaboration) . First evidence of ψ(2S)→Ω^-Ω⁺. Chinese Physics C, 2012, 36(11): 1040-1045. doi: 10.1088/1674-1137/36/11/002
[3]	Cristina Morales , on behalf , the NA . Recent results from NA48/2. Chinese Physics C, 2010, 34(6): 749-752. doi: 10.1088/1674-1137/34/6/023
[4]	for the . Status of KLOE-2. Chinese Physics C, 2010, 34(6): 918-923. doi: 10.1088/1674-1137/34/6/051
[5]	CHANG Zhe , GUAN Cheng-Bo . Statistical Properties of Radiation Fields in a Compact Space. Chinese Physics C, 2007, 31(9): 797-801.
[6]	ZHANG Xin , PAN Feng . Exact Solutions of sl-Boson System in U(2l+1) O(2l+2) Transitional Region. Chinese Physics C, 2002, 26(12): 1228-1237.
[7]	LI Xi-Guo , Marcello Baldo , SONG Jian-Jun , LIU Fang . Diffusion Equations in Lie Group Manifold. Chinese Physics C, 2001, 25(1): 86-88.
[8]	Huang Liangxin , Li Hong , Chen Tianlun . Further Study on SU(2)×SU(2) Lattice Chiral Model. Chinese Physics C, 1995, 19(3): 245-250.
[9]	YAN Jun , HU Shi-Ke . The Stable Compactification of Ten-Dimensional Supergravity Model. Chinese Physics C, 1993, 17(8): 692-699.
[10]	YU Zu-Rong . Irreducible Representations of Quantum Lie Superalgebra SL_q(2/1). Chinese Physics C, 1992, 16(11): 1035-1042.
[11]	YAN Jun , HU Shi-Ke . Compact Baby Universe Model in ten Dimension and Probability Function of Quantum Gravity. Chinese Physics C, 1991, 15(10): 890-897.
[12]	Chen Tianlun , Huang Wuqun , Jin Ke , Suo Cunchuan . β Function tor SU(2)×SU(2) Chiral Model on 2-Dimensional Random Triangle Lattice. Chinese Physics C, 1989, 13(S1): 43-48.
[13]	ZHU Zhong-Yuan , ZHANG Bo . TADPOLE DIAGRAM,ΔI=1/2 ENHANCEMENT AND ε′/ε. Chinese Physics C, 1988, 12(1): 50-54.
[14]	XU Jian-Jun , LI Xin-Zhou , NI Guang-Jiong . AN INFLATION SOLUTION FROM THE CALABI-YAU COMPACTIFICATION. Chinese Physics C, 1988, 12(6): 852-856.
[15]	SONG Xiao-Tong , CHING Cheng-Rui , HO Tso-Hsiu . APPROXIMATE B.S. WAVE FUNCTIONS FOR AN ELECTROMAGNETIC BOUND SYSTEM OF SPINS (1/2, 1/2) OR (1/2, 1/2) WITH UNEQUAL MASSES. Chinese Physics C, 1984, 8(5): 531-538.
[16]	SHEN Qi-Xing , WU Ji-Min , LU Jing-Xian , ZHAO Pei-Ying . THE BEHAVIOURS OF F₂^ep(X, Q²)-F₂^en(X, Q²) AND THE SCALE-BREAKING PARAMETER. Chinese Physics C, 1983, 7(3): 301-308.
[17]	Lu Jing-xian . 2π→2K SCATTERING AND πK ELASTIC SCATTERING. Chinese Physics C, 1980, 4(1): 28-32.
[18]	Sun Hong-zhou , Han Qi-zhi . ON THE IRREDUCIBLE REPRESENTATIONS OF THE SIMPLE LIE GROUPS I——THE TENSOR BASIS FOR THE INFINITESIMAL GENERATORS OF THE CLASSICAL SIMPLE LIE GROUPS. Chinese Physics C, 1980, 4(5): 588-599.
[19]	Sun Hong-zhou . ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(III). Chinese Physics C, 1980, 4(3): 271-285.
[20]	Sun Hong-zhou . ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(II). Chinese Physics C, 1980, 4(2): 137-159.

Access

Get Citation

Sun Hung-zhou. ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)[J]. Chinese Physics C, 1980, 4(1): 73-92.

Sun Hung-zhou. ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)[J]. Chinese Physics C, 1980, 4(1): 73-92. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1978-12-08
Revised: 1900-01-01

Article Metric

Article Views(2862)
PDF Downloads(333)
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

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

Peking University

Received Date: 1978-12-08

Accepted Date: 1900-01-01

Available Online: 1980-02-05

Abstract: In this paper, we analyse the commutation relations of the infintesimal opera-tors of the group SU₃ and find that the eight infinitesimal operators of the groupSU₃ can be written as a scalar operator A, three angular momentum operators (L₁,L_o, L_-1,)and two sets of the irreducible tensor operators of rank 1/2, （T_{±1/2，V_±1/2}）By means of the commutation relations of these operators, all irreducible represen-tations of the group SU₃ can be easily obtained. In this pape, the matrices corresponding to these operators in the irreduciblerepresentation（λμ）, are given; therefore the irreducible representation and its re-presentation space R^λμ are completely defined. Besides, a method for calculatingthe scalar factors of the reduction coefficients and the symmetric relations of thosefactors are also given. As examples, the scalar factors of the reduction coefficientsof （λμ）×（10）, （λμ）×（01）, （λμ）×（20） and （λμ）×（11） are calculated. In the last part of this paper, we define the irreducible tensor operators ofthe group SU₃ and prove the corresponding Wigner-Eckart theory. The method used in the discussion of the group SU₃ be extended to allof the compact simple Lie groups of rank 2 and we shall discuss them in two suc-ceeding papers.

HTML

Reference (1)

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

HTML

目录