Automated calculation of spin, isospin branching rules for su(4) irreps
S. Quintero, R. Henao, J. P. Valencia
TL;DR
The paper presents su4-branching, an open-source Python toolkit that automates the decomposition of high-dimensional SU$_{ST}$(4) irreps into spin–isospin ($S,T$) multiplets via Racah tensor-contraction, delivering complete branching rules with multiplicities and dimension checks. It combines rigorous group-theoretical machinery with a user-friendly notebook interface, enabling interactive exploration and reproducible workflows, including CSV and LaTeX exports and a CLI for batch use. Validation against classical tables (e.g., quesne1976, patera1981) and an exact dimensional-consistency condition ensure reliability for high-dimensional irreps, with benchmarks up to dimensions around $10^7$. The software supports nuclear structure, particle physics, and quantum chemistry studies by providing a general, multi-interface platform for SU$_{ST}$(4) branching, integration with U(6) ⊗ SU$_{ST}$(4) and U(10) ⊗ SU$_{ST}$(4) schemes, and a pathway for community contributions under the MIT license.
Abstract
The open-source Python package, su4-branching, is introduced for the derivation of comprehensive spin S and isospin T branching rules for any SU(4) irreducible representation.The Wigner supermultiplet scheme in nuclear and hadronic physics is based on SU(4) symmetry. However, the community does not have easy access to practical calculations of branching rules for any irreps.Our implementation combines group-theoretical methods with a notebook interface that is easy to use. This lets researchers look at large and complicated SU(4) irreps and check their work.The software produces tables, CSV files, and visual summaries, and it has been tested against both classic and modern reference results. This work enables group-structure investigations in nuclear modeling, particle physics, and quantum chemistry.