Abstract
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.
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