Local well-posedness of the coupled Yang-Mills and Dirac system in temporal gauge

Abstract

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].

20 gages. arXiv admin note: text overlap with arXiv:1506.02533, arXiv:2103.06770