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Investigate tensor operator matrix elements governed by the Wigner-Eckart theorem, assessing corrections under spontaneous symmetry breaking and testing for golden ratio asymptotics in high-spin limits.

August 14, 2026Open Access

Wigner-Eckart Theorem, Symmetry Breaking, and Golden Ratio in High-Spin Limits — E8 Intelligence Research

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ACAndrew Stewart Caldin

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Implication

Theoretical analysis evaluates tensor operators and symmetry breaking in high-spin quantum states, revealing standard asymptotic scaling without direct golden ratio geometric emergence.

Key Points

Investigate tensor operator matrix elements governed by the Wigner-Eckart theorem, assessing corrections under spontaneous symmetry breaking and testing for golden ratio asymptotics in high-spin limits.
Analyzed Wigner-Eckart theorem formulations, Clebsch-Gordan coefficients, and 3j symbols under broken group symmetry G → H.
Derived asymptotic limits for Clebsch-Gordan coefficients and reduced matrix element ratios as spin j approaches infinity.
Spontaneous symmetry breaking G → H generates direct mathematical corrections to reduced matrix elements.
High-spin limits produce standard asymptotic coefficient ratios of the form √(j/(j+1)) ≈ 1 − 1/(2j), yielding no direct golden ratio or base-60 geometric values.
Identified angular momentum algebraic links to the SO(3) root system (A₁) and spherical harmonics lattices.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a7ec735b70b84ec8b9135fa https://doi.org/10.5281/zenodo.21897919

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Implication

Theoretical analysis evaluates tensor operators and symmetry breaking in high-spin quantum states, revealing standard asymptotic scaling without direct golden ratio geometric emergence.

Wigner-Eckart Theorem, Symmetry Breaking, and Golden Ratio in High-Spin Limits — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

Wigner-Eckart Theorem, Symmetry Breaking, and Golden Ratio in High-Spin Limits — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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