Generalizations of Yang-Mills theory with nonlinear constitutive equations

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c → ∞) limits; we determine when such limits exist and obtain them explicitly