Open AccessPHYSICAL METHOD OF GROUP REPRESENTATION THEORY (IV)——THE IRREDUCIBLE BASES OF SU<sub>mn</sub>?SU<sub>m</sub>×SU<sub>n</sub> AND SU<sub>m+n</sub>?SU<sub>m</sub>?SU<sub>n</sub>
Author(s) -
Jinquan Chen,
Fan Wang,
GAO MEI-JUAN
Publication year - 1978
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.27.203
Subject(s) - special unitary group , physics , irreducible representation , combinatorics , group (periodic table) , mathematical physics , mathematics , quantum mechanics
It is proved that the CG coefficient of the permutation group and the outer-product reduction coefficient are just the coupling coefficient which couple the irreduci-ble basis of any SU(m) and SU(n), to those of SU(mn)?SU(m)× SU(n) and SU(m+n)?SU(m)?SU(n) respectively. Several simple methods are given for the calculation of the irreducible bases of SU(mn)?SU(m) × SU(n) and SU(m+n) ?SU(m)?SU(n) when using the Gelfand representation of SU(mn) and SU(m+n). The SU(6)?SU(3) × SU(2) and SU(8)?SU(4) × SU(2) baryon wave functions commonly used in elementary particle models are given in detail.