2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150800We express the Poisson brackets of local fields of the affine Toda field theories in terms of the Drinfeld-Sokolov dressing operator. For this, we introduce a larger space of fields, containing ``half screening charges'' and ``half integrals of motions''. In addition to local terms, the Poisson brackets contain nonlocal terms related to trigonometric r-matrices.32 pages, AMSLATEXQuantum AlgebraHigh Energy Physics - Theorytext