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This research aims to derive the quantum structure of the spin-3/2 sector under spectral admissibility constraints.

July 13, 2026Open Access

Quantum Structure beyond Spin-½: 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 under spectral admissibility constraints.
Investigated spectral admissibility on the binary icosahedral group 2I using generating set S = 10a ∪ 10b.
Derived implications of the Casimir operator for the normalization of spin-3/2 in comparison to spin-1/2.
Demonstrated co-admissibility of the spin-1/2 and spin-3/2 sectors and explored their behavior under admissibility refinement.
Both spin-1/2 and spin-3/2 sectors share the same Laplacian eigenvalue λ1/2 = λ3/2 = 18.
The emergence of SU(2) as a fixed point under the Born–Infeld spectral filter indicates a unique stable structural mechanism.
The representation-theoretic dimension test supplies a falsifiable prediction of r_eff = d².

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The randomized trial explores quantum structures in spin sectors, revealing their co-admissibility and implications for SU(2).

Jérôme Beau (2026) studied this question.

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