Wigner U(4)超多重群对称性的耦合与重新耦合系数
Coupling and Recoupling Coefficients for Wigner's U(4) Supermultiplet Symmetry
AI总结：
本文提出一种计算U(4)耦合和重新耦合系数的新方法，适用于U(4)对称系统，通过避免二项式系数和交替求和系列，实现快速准确的计算，同时探讨了U(4)不可约表示中(S,T)对的内多重性和外多重性。
摘要：
本文提出了一种新的方法，用于计算Wigner耦合系数和Racah重新耦合系数，适用于U(4)在两个子群链中的情况。所提出的程序避免了二项式系数和交替求和系列的使用，从而能够快速准确地计算任何U(4)相关的特征。通过SU(2)提升生成元的零空间维度获得(S,T)对的内多重性，而外多重性的解析则基于Alex等人关于U(N)的工作。预计最终将有一个C++库用于确定与U(4)的canonical和physical子群链相关的通用耦合和重新耦合系数。
英文摘要：
A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group-subgroup chains is presented. The canonical U(4)->U(3)->U(2)->U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4)->SU_S(2)xSU_T(2) coupling coefficients are more specific to nuclear structure studies that utilize Wigner's Supermultiplet Symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series, and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S,T) pair within a single U(4) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators; while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N). It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the \textit{canonical} and the \textit{physical} group-subgroup chains of U(4).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
