Unifying Qubit Symmetries: SU(2), Bloch Geometry, and Dissipative Semigroups — E8 Intelligence Research
Andrew Stewart Caldin
FINDING: Spin-1/2 qubit symmetries unify Lorentz/Poincaré group structure with Bloch sphere geometry via SU(2) representations, while dissipative dynamics extend the Bloch ball to gl(3,R)⊕R³ semigroup actions. | MATH: SU(2) ≅ Spin(3) double-covers SO(3); Bloch sphere S² ≅ SU(2)/U(1); Poincaré sphere = same SU(2) parameterization for polarization; dissipative semigroup: gl(3,R) ⊕ R³ acting on Bloch vector r ∈ ℝ³; fermionic time-reversal symmetry ⇒ trivial Bloch bundle (Z₂ index triviality); Wilson lines: holonomy ∮ A · dk over Brillouin zone torus. | CONNECTION: SU(2) binary polyhedral groups (binary tetrahedral 2T, octahedral 2O, icosahedral 2I) are finite subgroups of SU(2) — their orders (24, 48, 120) relate to crystallographic root systems (A₃, B₃, H₃). The icosahedral group 2I has golden ratio φ = (1+√5)/2 ≈ 1.618 embedded in its character table and quaternion generators; the Bloch sphere's equatorial projection yields stereographic ratios; dissipation's gl(3,R) contains SO(3) rota Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
•Sep 5, 2026•0 citations