SU(2) Symmetry: From Pauli Matrices to Quantum Gravity's Center Breaking — E8 Intelligence Research

FINDING: SU(2) representation theory provides the complete algebraic skeleton for spin, angular momentum, and gauge symmetries; the adjoint representation yields the so(3) algebra with structure constants ε_{ijk}, and the 2D fundamental representation is exactly the Pauli matrices. The Calabi–Yau paper extends this to center symmetry breaking in quantum gravity, linking higher-form symmetries to compactification geometry. | MATH: SU(2) generators satisfy [J_i, J_j] = i ε_{ijk} J_k. Irreducible representations labeled by j = 0, ½, 1, 3/2, … with dimension 2j+1. Pauli matrices σ_a/2 form the j=½ rep: σ_x σ_y − σ_y σ_x = 2i σ_z. Adjoint rep (j=1) has structure constants (T_a)_{bc} = −i ε_{abc}. Casimir J² = j(j+1)𝟙. Center of SU(2) is ℤ₂ = {±𝟙}; center symmetry breaking in Calabi–Yau compactifications involves ℤ_N factors from Wilson lines and higher-form gauge fields. | CONNECTION: The dimension formula 2j+1 yields the sequence 1, 2, 3, 4, 5, … — the integers themselves. The ratio of con

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com