2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108752A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some $(\pm)$associators for the product of some four operators is offered. The possible generalization of Hamilton's equations for a non-associative quantum theory is proposed. Some arguments are given that a non-associative quantum theory can be a fundamental unifying theory.8 pagesHigh Energy Physics - TheoryRings and AlgebrasQuantum Physicstext