2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55151A geometric formulation of the Moyal deformation for the Self-dual Yang-Mills theory and the Chiral Model approach to Self-dual gravity is given. We find in Fedosov's geometrical construction of deformation quantization the natural geometrical framework associated to the Moyal deformation of Self-dual gravity.LaTeX, mprocl.sty, 3 pages, no figures, version to appear in the Eighth Marcel Grossmann MeetingHigh Energy Physics - TheoryThe Geometry of Deformation Quantization and Self-Dual Gravitytext