Clebsch–Gordan Coefficients: No Direct Golden Ratio Connection Found — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are pedagogical and standard references on Clebsch–Gordan (CG) coefficients for SU(2) angular momentum addition, plus one research paper on the Jordanian deformation of su(2) affecting CG coefficients. No direct golden-ratio connection appears in the listed abstracts or titles. | MATH: CG coefficients: ⟨ j1 m1; j2 m2 | J M ⟩, satisfying |j1 − j2| ≤ J ≤ j1 + j2, M = m1 + m2. Recursion via ladder operators: J± |j m⟩ = √(j(j+1) − m(m± 1)) |j m± 1⟩. For j1 = j2 = 1/2: CG table yields singlet 1/√2(|↑↓⟩ − |↓↑⟩) and triplet 1/√2(|↑↓⟩ + |↓↑⟩) for M=0. Jordanian deformation Uh(sl(2)): generators H, X± with q-commutation relations, CG coefficients become h-dependent polynomials. | CONNECTION: No explicit golden ratio, Fibonacci, or base-60 appears. Howe
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026clebschgordan,
title = {{Clebsch–Gordan Coefficients: No Direct Golden Ratio Connection Found — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23554002},
url = {https://zenodo.org/records/23554002},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Clebsch–Gordan Coefficients: No Direct Golden Ratio Connection Found — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23554002
UR - https://zenodo.org/records/23554002
AB - FINDING: The search results are pedagogical and standard references on Clebsch–Gordan (CG) coefficients for SU(2) angular momentum addition, plus one research paper on the Jordanian deformation of su(2) affecting CG coefficients. No direct golden-ratio connection appears in the listed abstracts or titles. | MATH: CG coefficients: ⟨ j_1 m_1; j_2 m_2 | J M ⟩, satisfying |j_1 − j_2| ≤ J ≤ j_1 + j_2, M = m_1 + m_2. Recursion via ladder operators: J_± |j m⟩ = √(j(j+1) − m(m± 1)) |j m± 1⟩. For j_1 = j_2 = 1/2: CG table yields singlet 1/√2(|↑↓⟩ − |↓↑⟩) and triplet 1/√2(|↑↓⟩ + |↓↑⟩) for M=0. Jordanian deformation U_h(sl(2)): generators H, X_± with q-commutation relations, CG coefficients become h-dependent polynomials. | CONNECTION: No explicit golden ratio, Fibonacci, or base-60 appears. Howe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -