Symplectic Structure and Prequantum Bundles in Chern-Simons Theory — E8 Intelligence Research

FINDING: Chern-Simons theory quantization is governed by the Atiyah-Bott symplectic structure on the space of connections, with the integer level \(k\) as the symplectic form's cohomology class — the key insight is that the symplectic form \(ω = k/4π∫Σ Tr(δ A δ A)\) is not merely geometric but defines a prequantum line bundle whose curvature is \(k\) times a generator of \(H^2(A/G, Z)\). | MATH: Atiyah-Bott symplectic form: \(ωAB(α,β) = k/2π∫Σ Tr(α β)\) for \(α,β ∈ T_AA\); quantization condition: \([ωAB/2π] ∈ H^2(A/G, Z)\) forces \(k ∈ Z\). Combinatorial quantization (Aghaei) replaces the infinite-dimensional symplectic quotient with a finite-dimensional one using quantum groups, yielding the Reshetikhin-Turaev invariant with \(q = e2π i/(k+h^)\) where \(h^\) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com