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We present a new set of solutions to Yang-Mills equations with axially symmetric external charge sources. Our solutions for the gauge fields are not explicitly axisymmetric, but the noninvariance of the fields under a rotation about the symmetry axis can be compensated by a gauge transformation about a symmetry axis in gauge space. All gauge-invariant quantities are therefore axisymmetric. Our solutions are characterized by a gauge-invariant integer winding number {ital n}, and all winding numbers are allowed. We prove that the total gauge-invariant charge of the system (source plus gauge fields) vanishes identically in our solutions for {ital n}{ne}0, even if the source has net charge. We explicitly solve the equations of motion for a spherical shell of charge. The solution depends on the gauge coupling {ital g}, the total charge of the shell {ital Q}{sub {ital S}}, and the topological number {ital n}. We use perturbative methods to obtain the solution in closed form for {bar {alpha}}=={ital g}{sup 2}Q{sub S}/(4{pi}){much lt}1. We show analytically that in this limit the energy {ital scrE}{sub {ital n}} of the system satisfies the bound {ital scrE}{sub {ital n}}{le}(g{sup 2}Q{sub S}{sup 2}/(8{pi}a)){times}1/(2+1), where {ital a} is the radius of the shell. Using relaxation methods more » to find the exact solution to the equations of motion numerically for arbitrary {bar {alpha}}, we establish that this bound is satisfied for all {ital g}, {ital Q}{sub {ital S}}, and {ital n}. « less |
