  We consider the classical Yang-Mills system coupled with a Dirac equation in
3+1 dimensions in temporal gauge. Using that most of the nonlinear terms
fulfill a null condition we prove local well-posedness for small data with
minimal regularity assumptions. This problem for smooth data was solved forty
years ago by Y. Choquet-Bruhat and D. Christodoulou. The corresponding problem
in Lorenz gauge was considered recently by the author in [P1].
