Subduction of Baryon Spin into Octahedral Double-Group Irreps — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Lattice QCD baryon interpolators are classified by double-valued irreps of the octahedral group (Oh), requiring Clebsch–Gordan subduction from continuum SU(2) spin to the 48-element cubic point group. | MATH: Octahedral group order |Oh|=48; double group O_h^D has 48 elements, 8 irreps (A1,A2,E,T1,T2 × parity, plus spinor reps G1,G2,H). Subduction coefficients: ⟨J m | Λ λ⟩ where J=1/2,3/2,5/2,... and Λ ∈ {G1,G2,H} for half-integer J. Dimensions: G1(2), G2(2), H(4). For J=1/2 → G1; J=3/2 → H; J=5/2 → G2⊕H; J=7/2 → G1⊕G2⊕H. | CONNECTION: Octahedral group is the symmetry of the cube — its rotation axes are 4-fold (C4), 3-fold (C3), 2-fold (C2). The ratio of the number of spinor irreps to vector irreps (3 spinor vs 5 vector) echoes 3:5, related to the golden ratio via Fibonacci (3,5,8). The subduction coefficients themselves are square roots of rational numbers — e.g., for J=3/2→H, coefficients involve √(1/6), √(1/2), √(2/3) — denominators 6,2,3, whose reciprocals sum to 1 (1/6+1/2
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026subduction,
title = {{Subduction of Baryon Spin into Octahedral Double-Group Irreps — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587334},
url = {https://zenodo.org/records/23587334},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Subduction of Baryon Spin into Octahedral Double-Group Irreps — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587334
UR - https://zenodo.org/records/23587334
AB - FINDING: Lattice QCD baryon interpolators are classified by double-valued irreps of the octahedral group (Oh), requiring Clebsch–Gordan subduction from continuum SU(2) spin to the 48-element cubic point group. | MATH: Octahedral group order |Oh|=48; double group O_h^D has 48 elements, 8 irreps (A1,A2,E,T1,T2 × parity, plus spinor reps G1,G2,H). Subduction coefficients: ⟨J m | Λ λ⟩ where J=1/2,3/2,5/2,... and Λ ∈ {G1,G2,H} for half-integer J. Dimensions: G1(2), G2(2), H(4). For J=1/2 → G1; J=3/2 → H; J=5/2 → G2⊕H; J=7/2 → G1⊕G2⊕H. | CONNECTION: Octahedral group is the symmetry of the cube — its rotation axes are 4-fold (C4), 3-fold (C3), 2-fold (C2). The ratio of the number of spinor irreps to vector irreps (3 spinor vs 5 vector) echoes 3:5, related to the golden ratio via Fibonacci (3,5,8). The subduction coefficients themselves are square roots of rational numbers — e.g., for J=3/2→H, coefficients involve √(1/6), √(1/2), √(2/3) — denominators 6,2,3, whose reciprocals sum to 1 (1/6+1/2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -