Exact Classical Solution to the Yang-mills Equations with an External Source

In this paper, we are to investigate an SU(2) non-Abelian gauge field with an external source. If the external source is static and axisymmetric, we obtain the exact classical solution to the corresponding Yang-Mills equations. This solution has singularity at It can be seen that any particle, which carries an SU(2) gauge charge, becomes confined if it crosses into the region. Therefore the obtained solution exhibits the property of the SU(2) gauge charge confinement. From this classical solution, we also find the characteristic physical quantities of the SU(2) non-Abel gauge field coupled with the external source, namely gauge potentials, electromagnetic field intensities, external charge density and SU(2) non-Abel gauge field energy density. With the field function and topological index the SU(2) gauge potential corresponds to the potential of a point magnetic monopole