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This research aims to derive the quantum structure of the spin-3/2 sector while establishing the co-admissibility of spin-1/2 and spin-3/2 on the binary icosahedral group.

April 18, 2026Open Access

Quantum Structure beyond Spin-1/2: Co-Admissible Sectors and the Emergence of SU(2) as a Fixed Point

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This research aims to derive the quantum structure of the spin-3/2 sector while establishing the co-admissibility of spin-1/2 and spin-3/2 on the binary icosahedral group.
Introduced the spectral admissibility program on the binary icosahedral group.
Derived quantum mechanics of the spin-3/2 sector based on admissibility constraints.
Utilized the four-dimensional representation of $2I$ for derivation.
Examined the Casimir operator to normalize the Born rule.
Established that both spin-1/2 and spin-3/2 sectors share the same Laplacian eigenvalue of 18.
Confirmed co-admissibility of the two sectors on the binary icosahedral group.
Identified SU(2) as a unique stable sector under admissibility refinement.
Provided a falsifiable prediction with the representation-theoretic dimension test, $r_{\mathrm{eff}} = d^2$.

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Implication

This research derives quantum structure in spin-3/2 and confirms co-admissibility with implications for SU(2).

Cite This Study

Jérôme Beau (2026) studied this question.

synapsesocial.com/papers/69e3211640886becb65404f3 https://doi.org/10.5281/zenodo.19616445

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Quantum Structure beyond Spin-1/2: Co-Admissible Sectors and the Emergence of SU(2) as a Fixed Point

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Cite This Study

Quantum Structure beyond Spin-1/2: Co-Admissible Sectors and the Emergence of SU(2) as a Fixed Point

Key Points

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Implication

Cite This Study

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