Obtaining non-Abelian field theories via the Faddeev–Jackiw symplectic formalism

In this Letter we construct non-Abelian field theories employing the Faddeev–Jackiw symplectic formalism. The original Abelian fields were modified in order to introduce the non-Abelian algebra. We construct the SU(2)SU(2) and SU(2)⊗U(1)SU(2)⊗U(1) Yang–Mills theories having as starting point the U(1)U(1) Maxwell electromagnetic theory.