The Dirac and Gauge Yang-Mills Fields in Self-Consistent Consideration

TL;DR

This paper develops a self-consistent quasi-classical model of Dirac and Yang-Mills fields in SU(N) gauge theory, demonstrating solutions where fermion and gauge fields coexist and compensate each other's currents, with implications for QCD.

Contribution

It introduces a novel self-consistent quasi-classical framework for Dirac and Yang-Mills fields in SU(N) gauge theory, including exact solutions and their quantization.

Findings

Existence of self-consistent solutions for Dirac and YM fields at N≥3.

Fermion current compensates the gauge field current in solutions.

Application of the model to quantum chromodynamics (QCD).

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 (YM) equations containing the external fermion current are solved. The derived solutions are quantized in the quasi-classical approach. The developed model proves to have the self-consistent solutions of the Dirac and Yang-Mills equations at $N\geq 3$. Thereat the solutions take place provided that the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to it self-interaction. The obtained solution are considered in the context of QCD.