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=Q₁ is the point of bifurcation between the two nondegenerate non-Abelian solutions and a Coulomb-type solution, (ii) for Q₁< Q<Q₂, E_NA^I<E_C<E_NAII, (iii) for Q=Q₂, E_NA^I<E_C=E_NAII, (iv) for Q> Q₂, E_NA^II<E_NA^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.