Knot Polynomials from QFT and Quantum Groups — E8 Intelligence Research

FINDING: Knot invariants from zero-dimensional QFT and quantum groups yield polynomial invariants (Jones, HOMFLY-PT, Alexander) that encode topological data of embeddings in 3-space. | MATH: Jones polynomial \( V_K(t) \) satisfies skein relation \( t⁻¹VL_+ - tVL_- = (t1/2 - t-1/2)VL_0 \); Alexander polynomial \( Δ_K(t) \) from Seifert matrix; HOMFLY-PT polynomial \( P_K(a,z) \) generalizes both. Quantum invariants from \( U_q(sl_2) \) at roots of unity give 3-manifold invariants (Witten-Reshetikhin-Turaev). | CONNECTION: Jones polynomial evaluated at \( t = e2π i/5 \) yields golden ratio \( φ = 1.618... \) for certain knots (e.g., \( VT(2,5)(e2π i/5) = φ \)); Alexander polynomial relates to Seifert surfaces and linking numbers, echoing base-60 sexagesimal cycles in periodicity. | DEPTH: 7 — Bridges quantum field theory, topology, and number theory; golden ratio emergence suggests deeper geometric harmony in knot spectra. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com