2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202593Weinberg's theorem for π-πscattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold π-πscattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.10 pages, 7 figures, Revtex 3High Energy Physics - Phenomenologytext