Chern-Simons Wilson Loops Link Knot Invariants to Topological Quantum Computing — E8 Intelligence Research

FINDING: Wilson loops in Chern-Simons theory produce knot invariants (Jones polynomial) that directly encode topological quantum computing braiding operations via anyon world-lines. | MATH: Chern-Simons action \( SCS = k/4π ∫_M Tr(A dA + 2/3 A A A) \), level \( k ∈ Z \) (integer quantization). Wilson loop expectation value \( W_R(K) = {∫ DA \, W_R(K) e^{iSCS}}{∫ DA \, e^{iSCS}} \) yields knot polynomial (e.g., Jones polynomial for \( SU(2) \)). Braid group generators \( σ_i \) satisfy \( σ_i σᵢ₊₁ σ_i = σᵢ₊₁ σ_i σᵢ₊₁ \) (Yang-Baxter equation). | CONNECTION: Jones polynomial evaluated at roots of unity (e.g., \( q = e2π i/(k+2) \)) gives quantum invariants linked to golden ratio \( φ = 1.618 \) when \( k=3 \) (Fibonacci anyons: \( φ^2 = φ+1 \)). Braiding matrices have eigenvalues \( e± 4π i/5 \), related to \( 0.618 \) and \( 1.6 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com