Hyperfine Coupling Ratio Unity Reveals SU(2) Symmetry in Qubit Spin Dynamics — E8 Intelligence Research

Abstract

FINDING: Hyperfine coupling ratio near unity in qubit control reflects SU(2) symmetry, linking spin dynamics to geometric phase and coupling constant ratios. | MATH: SU(2) generators satisfy \([J_i, J_j] = i \epsilon_{ijk} J_k\); hyperfine coupling constant \(A\) defines Hamiltonian \(H = A \mathbf{I} \cdot \mathbf{J}\); ratio \(A_1/A_2 \approx 1\) implies near-degenerate eigenstates; spin pumping current \(\mathbf{J}_s \propto \mathbf{m} \times \dot{\mathbf{m}}\) yields geometric (Berry) phase. | CONNECTION: SU(2) symmetry maps to quaternion rotations on 3-sphere; ratio 1:1 corresponds to tetrahedral symmetry (root system \(A_3\), Coxeter number 4); geometric phase factor \(\exp(i \Omega/2)\) with solid angle \(\Omega\) relates to golden ratio via \(\Omega = 2\pi(1-1/\phi)\) for certain paths (0.618, 1.618). | DEPTH: 7 — Direct link between coupling constant ratio unity and SU(2) geometric phase is known but not fully exploited; connection to golden ratio in spin precession paths is s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com