Automated calculation of spin–isospin branching rules for SU(4) irreps

The open-source Python package su4-branching automates the derivation of comprehensive spin S and isospin T branching rules for SU(4) irreducible representations. The Wigner supermultiplet scheme underlying nuclear and hadronic physics depends critically on SU(4) symmetry. However, practical calculations of branching rules for arbitrary SU(4) irreps have been largely inaccessible to the research community. Our implementation combines Racah’s tensor contraction formula with Python modularity, enabling straightforward exploration of high-dimensional SU(4) irreps through interactive Jupyter interfaces and multiple export formats. Comprehensive validation against three independent reference frameworks (Quesne 1976; Patera 1981; Pan et al. 2024) and dimensional consistency checks (necessary and sufficient for correctness) demonstrate reliability across dimensions 1–10^7. This work enables systematic group-theoretical investigations in nuclear structure, particle physics, and quantum chemistry.开源Python包su4-branching可自动推导SU(4)不可约表示下完备的自旋S与同位旋T分支规则。核物理与强子物理的核心框架——维格纳超多重态方案，其有效性高度依赖SU(4)对称性。然而此前科研界难以实现任意SU(4)不可约表示分支规则的实用化计算。本实现将拉卡（Racah）张量收缩公式与Python模块化特性相结合，可通过交互式Jupyter界面与多种导出格式，便捷地探索高维SU(4)不可约表示。本工作通过与三个独立参考框架（Quesne 1976、Patera 1981、Pan等人2024年研究）的全面比对，以及维度一致性检验（正确性的充要条件），验证了其在1至10^7维度范围内的可靠性。该成果可为核结构、粒子物理与量子化学领域的系统群论研究提供有力支撑。