Wigner–Eckart Theorem: Core Math Behind Topological-Sector Finite-Size Corrections — E8 Intelligence Research

FINDING: The search results are dominated by pedagogical videos and a single arXiv paper on finite magnetic groups — no direct hit on the topological-sector finite-size corrections from arXiv:2007.03539. The core mathematical content is the Wigner–Eckart theorem itself: matrix elements of irreducible tensor operators factor into a Clebsch–Gordan coefficient (geometry of angular momentum coupling) and a reduced matrix element (physics). | MATH: ⟨j′m′|T^k_q|jm⟩ = ⟨j′‖T^k‖j⟩ · ⟨j k; m q | j′ m′⟩ — the CG coefficient is a ratio of integers (or half-integers) derived from SU(2) representation theory; the reduced matrix element is independent of m, m′, q. For finite magnetic groups (arXiv:0911.0276v1), the theorem generalizes to antiunitary symmetries, requiring corepresentations and modified CG coefficients. | CONNECTION: The CG coefficients for SU(2) are intimately tied to the quantum numbers j, m — these are half-integers, and the recursion relations involve ratios like √(j±m)(j±m+1) — no Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com