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

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

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

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

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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.

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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

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Received: 1977-11-05
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

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）.