A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF <EM>SU<SUB>n</SUB></EM> GROUP

CHEN JIN-QUAN; YU ZU-RONG; WANG FAN

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> 1979, Vol. 3> Issue(2) : 216-255

A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SU_n GROUP

Abstract
HTML
Reference
Related

PDF

Abstract：
It is proved that under the Gelfand-Biedenharn phase convention any SU_n singletfactor （SF） belongs to the type of the derivable or underivable,designated as （SU_nSF）d and （SU_r SF） respectively,and （SU_n SF）d=（SU_r SF）,n=r+1,r+2,….Therefore the calculation of any SU_n Clebsch-Gordan coefficients is reduced to thecalculation of a few underivable singlet factor （SU_r SF）.

References

[1]

陈金全、王凡、高美娟，物理学报，27(1978), 31.[2] J. J. De Swart, Rev. Mod. Phys., 35 (1963), 916.[3] E. M. Haacke, J. W.Moffat and P. Savaria, J. Math Plays.,17 (1976), 2041.[4] I. M. Gelfand and M.L. Tseitlin, "Dokl. Akad Nauk. SSSR"71 (1950), 825. G. E. Baird and L.C. Biedenharn, J. Math. Phys., 5 (1964),1723.[5] 陈金全、王凡、高美娟，物理学报，26(1977), 427.[6] G. Racah, Phys Rev., 76 (1949), 1352. "Group Theory and Spectroscopy" (1951), Princeton.

[1]	LIU Da-Qing . Compute the Real Orthogonal Form of [n—1,1] Representation of S_n Group in a Special Representation Space. Chinese Physics C, 2007, 31(12): 1099-1101.
[2]	Lu Hong , Liu Shaomin , Dang Linkal , Mu Jun , Wang Hui , Feng Zhenyong , Ren Jingru , Xu Xianwu , Yu Guangce , Zhou Wendel , , , , , , . The Correlation Between the Deviation of Sun’s Shadows and the Mean Solar Magnectic Field. Chinese Physics C, 1999, 23(4): 313-319.
[3]	Liu Shaomin , Ding Linkai , Shi Ce , Mu Jun , Wang Hui , Lu Hong , Feng Zhenyong , Ren Jingru , Yu Guangce , Zhou Wende , Meng Xia , , , , , . Correlation Between Sun Shadows of 10TeV Cosmic Rays and Solar Activity. Chinese Physics C, 1997, 21(10): 865-867.
[4]	Liu Shaomin , Ding Linkai , Shi Ce , Zhaxiciren , Zhaxisanzhu , Mu Jun , Wnag Hui , Lu Hong , Feng Zhenyong , Ren Jingru , Yu Guangce , Zhou Wende , Labaciren , Meng Xianru , Meng Lie , Zhang Jilong , Zhang Chunsheng , Zhang Huimin , Shi Zhizheng , Jia Huanyiu , Mei Dongming , Huang Qing , Tan Youheng , Huo Anxiang , Dai Benzhong . Correlation Between Sun Shadows of 10 TeV Cosmic Ray and the Solar Activity. Chinese Physics C, 1997, 21(S4): 11-18.
[5]	Wu Lianao , Liu Gang . A New Formula for the Spectra of Axial Symmetric and Transition Nuclei and a Quantity to Identify the Nuclear γ Deformation. Chinese Physics C, 1996, 20(4): 339-344.
[6]	Zhang Jun , Yang Guangcan , Yan Hong . 2-Dimensional Cyclic Representations of U_q(sl(2)), C-GCoefficients and a Free Fermion 8-Vertex Model. Chinese Physics C, 1995, 19(12): 1084-1089.
[7]	Zhong Yunxiao , Hu Jimin . Study of the Multidimensional Kramers'Equation. Chinese Physics C, 1994, 18(10): 949-954.
[8]	Lin Fumin , Su Rukeng , Song Hongqiu . Comment on the Formula of β-stability Line. Chinese Physics C, 1994, 18(8): 745-747.
[9]	XU Fuxin , XU Ni . A Comprehensive Analysis for Eight Formulas for Rotational Spectra. Chinese Physics C, 1993, 17(11): 1040-1047.
[10]	MENG Jie , YIN Chuan-Zong , LIN Xin-Wei . A Simple Formula for Backbending. Chinese Physics C, 1991, 15(12): 1109-1114.
[11]	PAN Feng . ANALYTICAL EXPRESSIONS OF SOME MULTIPLICITY-FREE ISOSCALAR FACTORS FOR SU_N SO_N UNDER THE ORTHOGONAL BASIS. Chinese Physics C, 1990, 14(9): 851-854.
[12]	LU Hai-Tao , Diao Hao , ZHANG Mao-Lin . A SYNTHESIS LEVEL DENSITY FORMULA. Chinese Physics C, 1988, 12(3): 396-403.
[13]	MIAO Rong-Zhi , WU Guo-Hua , ZHENG Wei-Han , LIU Jian-Ye , YU Chao-Fan , YU Xie . A MODIFICATION FOR COMPLEX-PARTICLE EMISSION PROBABILITY IN THE PRE-EQUILIBRIUM EXCITON MODEL. Chinese Physics C, 1985, 9(1): 95-100.
[14]	YU Zu-Rong . TRANSFORMATION COEFFICIENTS BETWEEN SO(6) AND SU(4) GELFAND-ZETLIN STATES. Chinese Physics C, 1983, 7(1): 121-125.
[15]	ZENG GAO-JIAN . A GENERAL FORMULA ON C-G SERIES OF U(3) GRONP. Chinese Physics C, 1982, 6(1): 113-116.
[16]	FENG REN-FA , WU XI-ZHEN , ZHANG XI-ZHEN , ZHUO YI-ZHONG . MICROSCOPIC CALCULATION OF VISCOSITY COEFFICIENT IN HEAVY NUCLEI. Chinese Physics C, 1981, 5(3): 346-351.
[17]	Zheng Jin-yan , Cheng Tan-sheng , Yang Fu-jia . FURTHER STUDY ON NUCLEAR MASS FORMULA. Chinese Physics C, 1980, 4(5): 632-639.
[18]	ZHAO SHU-SONG , PENG SHOU-LI , YU CHUAN-ZAN . SCALING PHENOMENA AND RENORMALIZATION GROUP. Chinese Physics C, 1979, 3(4): 387-392.
[19]	CHEN JIN-QUAN , GAO MEI-JUAN , WANG FAN . ON THE PHASE AND THE REPRESENTATION TRANSFORMATIONS OF SU_n BARYON AND MESON WAVE FUNCTIONS. Chinese Physics C, 1979, 3(4): 408-417.
[20]	GU CHAO-HAO . THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES. Chinese Physics C, 1978, 2(4): 295-304.

Access

Get Citation

CHEN JIN-QUAN, YU ZU-RONG and WANG FAN. A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SU_n GROUP[J]. Chinese Physics C, 1979, 3(2): 216-255.

CHEN JIN-QUAN, YU ZU-RONG and WANG FAN. A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SU_n GROUP[J]. Chinese Physics C, 1979, 3(2): 216-255. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1977-11-05
Revised: 1900-01-01

Article Metric

Article Views(2213)
PDF Downloads(266)
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

A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SU_n GROUP

Received Date: 1977-11-05
Accepted Date: 1900-01-01
Available Online: 1979-04-05

Abstract: It is proved that under the Gelfand-Biedenharn phase convention any SU_n singletfactor （SF） belongs to the type of the derivable or underivable,designated as （SU_nSF）d and （SU_r SF） respectively,and （SU_n SF）d=（SU_r SF）,n=r+1,r+2,….Therefore the calculation of any SU_n Clebsch-Gordan coefficients is reduced to thecalculation of a few underivable singlet factor （SU_r SF）.