Sum rules for the matrices of the generators of SU(3) in an SO(3) basis
Sum rules for the matrices of the generators of SU(3) in an SO(3) basis
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SO(3) 基础上 SU(3) 生成元矩阵的求和规则
DOI：
10.1063/1.523967
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发表时间：
1979
影响因子：
1.3
通讯作者：
C. Quesne
中科院分区：
文献类型：
--
作者：
A. Partensky;C. Quesne
我们考虑半约化的各种求和规则，在对应于群约化SU（3）<$SO（3）<$SO（2）的不可约表示[pq]的基础上，相对于SO（3）约化SU（3）的生成元的矩阵元素。我们使用的基本状态对角化一个额外的标签操作员K，但避免其明确的建设。我们从两个独立的SU（3）向量算子X和V构建所有需要的算子，其中X=（L，Q）由SU（3）生成元组成，V=（VL，VQ）根据它们定义。首先给出了Q的对角半约化矩阵元所满足的线性和规则的解析公式。然后，从Q和VQ的半约化矩阵元所满足的二次方程组中，我们得到了这些量所满足的二次和规则的显式表达式。所有上述求和规则都与K的选择无关。当K被定义为三阶算子L.VL时，我们证明了一些非对角算子之间的关系。
We consider various sum rules for the semireduced [i.e., reduced with respect to SO(3)] matrix elements of the generators of SU(3) in a basis of an irreducible representation [pq] corresponding to the group reduction SU(3) ⊆SO(3) ⊆SO(2). We use basis states which diagonalize an additional labeling operator K, but avoid their explicit construction. We build all the needed operators from the two independent SU(3) vector operators X and V, where X= (L,Q) is made of the SU(3) generators and V= (VL, VQ) is defined in terms of them. First we obtain an analytical formula for the linear sum rule satisfied by the diagonal semireduced matrix elements of Q. Then, from the set of quadratic equations fulfilled by the semireduced matrix elements of Q and VQ, we obtain explicit expressions for the quadratic sum rules satisfied by these quantities. All the above‐mentioned sum rules are independent of the selection made for K. When K is defined as the third order operator L.VL, we show that a relation between some nondiag...