Programs for generating Clebsch–Gordan coefficients of SU(3) in SU(2) and SO(3) bases
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Abstract Computer codes are developed to calculate Clebsch–Gordan coefficients of SU(3) in both SU(2)- and SO(3)-coupled bases. The efficiency of this code derives from the use of vector coherent state theory to evaluate the required coefficients directly without recursion relations. The approach extends to other compact semi-simple Lie groups. The codes are given in subroutine form so that users can incorporate the codes into other programs. Title of program: SU3CGVCS Catalogue Id: ADTN_v1_0 Nature of problem The group SU(3) and its Lie algebra su(3) have important applications, for example, in elementary particle physics , nuclear physics, and quantum optics. The code presented is particularly relevant for the last two fields. Clebsch-Gordan (CG) coefficients are required whenever the symmetries of many-body systems are used for the evaluation of matrix elements of tensor operators. Moreover, the construction of CG coefficients for SU(3) serves as a nontrivial prototype for larger compact semi-simpl ... Versions of this program held in the CPC repository in Mendeley Data ADTN_v1_0; SU3CGVCS; 10.1016/j.cpc.2004.01.005 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)
【摘要】 本研究开发了用于计算SU(3)群在SU(2)耦合基与SO(3)耦合基下的克利布施-戈登（Clebsch–Gordan）系数的计算机程序代码。该代码的高效性源于采用矢量相干态（vector coherent state）理论，可直接计算所需系数，无需使用递推关系。该方法可推广至其他紧致半单李群。代码以子程序形式提供，便于用户将其集成至其他程序中。 程序名称：SU3CGVCS 目录编号：ADTN_v1_0 问题属性 SU(3)群及其李代数su(3)具有重要应用场景，例如在粒子物理、核物理与量子光学领域，本代码尤其适用于后两个研究方向。当利用多体系统的对称性计算张量算子的矩阵元时，均需用到克利布施-戈登（Clebsch-Gordan, CG）系数。此外，SU(3)群的CG系数构建可作为更大规模紧致半单李群相关问题的非平凡原型。 存放在Mendeley数据平台CPC库中的该程序版本：ADTN_v1_0；SU3CGVCS；DOI: 10.1016/j.cpc.2004.01.005 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）。
