Canonical solution of the state labelling problem for SU(n) SO(n) and Littlewood's branching rule. III. SU(3) SO(3) case
Canonical solution of the state labelling problem for SU(n) SO(n) and Littlewood's branching rule. III. SU(3) SO(3) case
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SU(n) SO(n) 和 Littlewood 分支规则的状态标记问题的规范解。
DOI：
10.1088/0305-4470/17/4/019
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
C. Quesne
中科院分区：
文献类型：
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作者：
C. Quesne
第二部分见同上，第17卷，第4期，第777 -89页（1984）。第一部分和第二部分讨论了一般条款的一个新的解决方案的状态标签问题的d行不可约表示（irreps）的SU（n），当减少对SO（n）。这个解被称为正则解，因为它以一种直接的方式反映了Littlewood分支规则对U（n）<$O（n）的运算。本文详细地讨论了SU（3）→ SO（3）情形。得到了SO（3）irrep（h ~ 1h ~ 2）的正则基态的显式表达式。计算了从Bargmann-Moshinsky基到正则基的变换矩阵。结果表明，在这两种情况下，在将乘积表示jL × js约化为SU（2）irreps j的过程中，完全指定状态所需的额外标号js可以被选择作为表征“中间”SU（2）irrep的标号js，其中j = 1/2（h1-h2），jL = 1/2L或1/2（L - 1），无论h1 + h2 - L是偶数还是奇数。
For pt.II see ibid., vol.17, no.4, p.777-89 (1984). Parts I and II discussed in general terms a new solution to the state labelling problem for the d-row irreducible representations (irreps) of SU(n), when reduced with respect to SO(n). This solution was termed canonical because it reflects the operation of Littlewood's branching rule for U(n) ⊃ O(n) in a straightforward way. The SU(3) ⊃ SO(3) case is now worked out in detail. Explicit expressions of the canonical basis states of SO(3) irreps L belonging to an SU(3) irrep (h1h2) are obtained. The matrix of the transformation from the Bargmann-Moshinsky basis to the canonical one is also calculated. It is shown that in both cases the extra label necessary to completely specify the states can be chosen as the label js characterising an 'intermediate' SU(2) irrep in the reduction of the produce representation jL × js into SU(2) irreps j, where j = 1/2(h1-h2) and jL = 1/2L or 1/2(L - 1) whenever h1 + h2 - L is even or odd.