What question did this study set out to answer?

To determine how spontaneous symmetry breaking modifies standard Wigner-Eckart matrix element relations in high-spin quantum systems.

August 15, 2026Open Access

Spontaneous Symmetry Breaking Corrections to Wigner-Eckart Relations in High-Spin Systems — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Theoretical analysis demonstrates spontaneous symmetry breaking corrections to Wigner-Eckart relations in high-spin systems, indicating size-dependent deviations driven by Goldstone modes.

Key Points

To determine how spontaneous symmetry breaking modifies standard Wigner-Eckart matrix element relations in high-spin quantum systems.
Analyzed matrix element corrections arising from continuous symmetry breaking (such as SU(2) breaking to U(1)) and associated Goldstone modes.
Calculated size scaling relations as a function of system size L and spatial dimension d.
Evaluated Clebsch-Gordan coefficients and angular momentum recoupling in the high-spin asymptotic limit (j >> 1).
Matrix element corrections scale inversely with system size (proportional to 1/L^d) and directly with the symmetry-breaking order parameter.
Recoupling coefficients under SU(2) to U(1) breaking converge toward golden ratio relationships (approaching 0.618 and 1.618) in the high-spin limit.
Underlying condensed matter crystal lattices, including cubic and hexagonal structures, impose discrete boundary constraints on the correction terms.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a8019fe75c2e31742c86552 https://doi.org/10.5281/zenodo.21912909

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Implication

Theoretical analysis demonstrates spontaneous symmetry breaking corrections to Wigner-Eckart relations in high-spin systems, indicating size-dependent deviations driven by Goldstone modes.

Spontaneous Symmetry Breaking Corrections to Wigner-Eckart Relations in High-Spin Systems — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

Spontaneous Symmetry Breaking Corrections to Wigner-Eckart Relations in High-Spin Systems — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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