Construction of nondegenerate non-Abelian solutions and Coulomb-type solution for the same charge distribution in SU(2) Yang-Mills theory.

Abstract

We propose a new cylindrical ansatz for SU(2) Yang-Mills theory which lifts the degeneracy between the two non-Abelian solutions in the presence of a time-independent charge current. We then construct explicit solutions for which we find that (i) Q=${Q}_{1}$ is the point of bifurcation between the two nondegenerate non-Abelian solutions and a Coulomb-type solution, (ii) for ${Q}_{1}$${Q}_{2}$, ${E}_{\mathrm{NA}{}^{\mathrm{I}{E}_{C}{E}_{\mathrm{NA}{}^{\mathrm{II}}}}}$, (iii) for Q=${Q}_{2}$, ${E}_{\mathrm{NA}{}^{\mathrm{I}{E}_{C}={E}_{\mathrm{NA}{}^{\mathrm{II}}}}}$, (iv) for Q>${Q}_{2}$, ${E}_{\mathrm{NA}}^{\mathrm{II}}$${E}_{\mathrm{NA}}^{\mathrm{II}}$${E}_{C}$. Here Q is the gauge-invariant charge and E is the total energy. Finally, we show that our ansatz is related to the usual cylindrical ansatz by a nonsingular gauge transformation.