Unified Closed-Form Representations and Generating Functionals for SU(2) 3n-j Recoupling Coefficients
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866902122875846656 |
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| author | Sherrington, Ryan |
| author_facet | Sherrington, Ryan |
| contents | <div> <div>We present a unified framework for computing SU(2) 3nj recoupling coefficients through five complementary mathematical representations: hypergeometric product formulas, uniform single-sum expressions, finite recurrence relations, universal generating functionals, and arbitrary-valence matrix elements. This work establishes the first truly closed-form expressions for arbitrary trivalent graphs, validated through rigorous cross-verification against symbolic computation and high-precision reference datasets. Applications span quantum physics from atomic structure to loop quantum gravity.</div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18489844 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Unified Closed-Form Representations and Generating Functionals for SU(2) 3n-j Recoupling Coefficients Sherrington, Ryan Wigner Symbols 3nj Coefficients Angular Momentum Recoupling Hypergeometric Functions Generating Functionals Spin Networks Numerical Stability Uncertainty Quantification SU(2) Angular Momentum Angular Momentum Coupling Recoupling Theory 3nj Symbols Wigner 3j Wigner 6j Wigner 9j Clebsch–Gordan Coefficients Racah Coefficients Regge Symmetries Generating Function Graphical Methods Quantum Mechanics Computational Physics Symbolic Computation Recoupling Coefficients 3n-j symbols generating functionals hypergeometric functions <div> <div>We present a unified framework for computing SU(2) 3nj recoupling coefficients through five complementary mathematical representations: hypergeometric product formulas, uniform single-sum expressions, finite recurrence relations, universal generating functionals, and arbitrary-valence matrix elements. This work establishes the first truly closed-form expressions for arbitrary trivalent graphs, validated through rigorous cross-verification against symbolic computation and high-precision reference datasets. Applications span quantum physics from atomic structure to loop quantum gravity.</div> </div> |
| title | Unified Closed-Form Representations and Generating Functionals for SU(2) 3n-j Recoupling Coefficients |
| topic | Wigner Symbols 3nj Coefficients Angular Momentum Recoupling Hypergeometric Functions Generating Functionals Spin Networks Numerical Stability Uncertainty Quantification SU(2) Angular Momentum Angular Momentum Coupling Recoupling Theory 3nj Symbols Wigner 3j Wigner 6j Wigner 9j Clebsch–Gordan Coefficients Racah Coefficients Regge Symmetries Generating Function Graphical Methods Quantum Mechanics Computational Physics Symbolic Computation Recoupling Coefficients 3n-j symbols generating functionals hypergeometric functions |
| url | https://doi.org/10.5281/zenodo.18489844 |