Abstract
The quasi‐classical model in a gauge theory with the Yang‐Mills (YM) field is developed. On a basis of the exact solution of the Dirac equation in the SU(N) gauge field which is in the eikonal approximation the Yang‐Mills equations containing an external current are solved. The developed model proves to have the self‐consistent solutions of the Dirac and Yang‐Mills equations at N≥3. The derived solutions take place provided that the fermion and gauge fields exist together, so that the fermion current completely compensates the current generated by the gauge field due to its self‐interaction. The obtained solutions are considered in the context of QCD.
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