The self-consistent quasi-classical model in SU(N) gauge field theory

The quasi-classical model in a gauge theory with the Yang-Mills (YM) field is developed. The self-consistent solutions of the Dirac equation in the external SU(N) gauge field and the Yang-Mills equations containing the external fermion current are obtained when the the Yang-Mills field is in the eikonal approximation. The derived solutions are quantized in the quasi-classical approach. It is shown that the solutions take place provided that the dimension of the gauge group is N⩾3. In this way, the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to its self-interaction. The obtained solution are considered in the context of QCD.