A numerical algorithm for the explicit calculation of SU(N) and SL(N,\mathbb C)SL(N,C) Clebsch–Gordan coefficients

2010/09/30 by Arne Alex, Matthias Kalus, Alan Huckleberry +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Code (set theory) #Exposition (narrative) #Numerical analysis #Numerical integration #Numerical stability #Representation (politics) #Source code #cond-mat.other #hep-th #math-ph #math.MP #math.RT #nucl-th

paper · pdf · doi:10.1063/1.3521562

published as J. Math. Phys. 52:023507,2011 · 35 pages, 3 figures, 5 tables

openalex publication_date 2011/02/01 · arxiv created 2011/03/28 · arxiv updated 2011/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present an algorithm for the explicit numerical calculation of SU(N) and \documentclass[12pt]minimal\begindocumentSL(N,\mathbb C)\enddocumentSL(N,C) Clebsch–Gordan coefficients, based on the Gelfand–Tsetlin pattern calculus. Our algorithm is well suited for numerical implementation; we include a computer code in an appendix. Our exposition presumes only familiarity with the representation theory of SU(2).

Citations

• Group theory for unified model building
• Density matrix numerical renormalization group for non-Abelian symmetries
• Theory of Complex Spectra. II

Cited by

• Simple factorization of unitary transformations
• The light scalar mesons as tetraquarks
• An efficient high dimensional quantum Schur transform
• Density matrix renormalization group simulations of SU(N) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz
• Clebsch–Gordan coefficients [wikipedia]

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