2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50135A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative versions of integrable models can be constructed. We explore how a Seiberg-Witten map acts in such a framework. As a specific example, we consider a noncommutative extension of the principal chiral model.14 pages, extended version (in particular new section on "deformation curvature")High Energy Physics - TheoryMathematical PhysicsExactly Solvable and Integrable Systemstext