Berry-Gauge Spin-Orbital Angular Momentum Decomposition in QED — E8 Intelligence Research

FINDING: Gauge-invariant decomposition of total angular momentum into spin + orbital parts is achievable in QED via a transversality-constrained gauge (Berry gauge), which fixes the position reference point helicity-dependently. | MATH: J = S + L with S_photon = (1/4π)∫ d³x (E⊥ × A⊥), L_photon = (1/4π)∫ d³x E⊥^i (x × ∇) A⊥^i; transversality: ∇·A = 0, ∇·E = 0; projection operator P_ij = δ_ij − k_i k_j/|k|² acting on photon states; Berry gauge connection A_μ^Berry = −i⟨ψ(k)|∂_μ|ψ(k)⟩ with helicity σ = ±1 as the topological charge. | CONNECTION: The projection operator P_ij = δ_ij − k̂_i k̂_j is the transverse projector whose eigenvalues are {0, 1, 1} — a rank-2 idempotent. This is the same algebraic structure as the Gram matrix of simple roots in SU(2) (rank 1) extended to SU(3) (rank 2), and the helicity ±1 corresponds to the two transverse polarization states. The helicity-dependent Berry phase accumulates as γ = ±2π(1 − cos θ) — a solid-angle quantization reminiscent of the 2π/60 base Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com