Optical Absorption Probes Interaction-Dressed Quantum Metric and Berry Curvature — E8 Intelligence Research

FINDING: Optical absorption directly measures the interaction-dressed quantum metric and Berry curvature in solids, unifying quantum geometry with many-body physics. | MATH: Quantum geometric tensor: Q_μν = g_μν + (i/2)F_μν, where g_μν = Re[⟨∂_μu|(1−P)|∂_νu⟩] (quantum metric) and F_μν = Berry curvature. Optical conductivity: σ_ab(ω) ∝ Σ ∫ dk g_ab(k) δ(ħω − ΔE(k)) for metric contribution; σ_ab^A(ω) ∝ ε_abc F_c(k) for curvature (anomalous) contribution. Interaction dressing: g_μν → g_μν + δg_μν^(int), F_μν → F_μν + δF_μν^(int) via vertex corrections (Feynman diagrams). | CONNECTION: Quantum metric g_μν defines a Riemannian structure on the Brillouin zone (parameter space manifold). Berry curvature F_μν is the associated symplectic/Kähler form. Together they form a Kähler manifold structure — the natural geometric harmony is the ratio g/F (metric-to-curvature), analogous to the ratio of real to imaginary parts in complex geometry. In 2D, the Fubini-Study metric satisfies g_xx + g_yy = |F_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com