  Scattering methods make it possible to compute the effects of renormalized
quantum fluctuations on classical field configurations. As a classic example of
a topologically nontrivial classical solution, the Abrikosov-Nielsen-Olesen
vortex in U(1) Higgs-gauge theory provides an ideal case in which to apply
these methods. While physically measurable gauge-invariant quantities are
always well-behaved, the topological properties of this solution give rise to
singularities in gauge-variant quantities used in the scattering problem. In
this paper we show how modifications of the standard scattering approach are
necessary to maintain gauge invariance within a tractable calculation. We apply
this technique to the vortex energy calculation in a simplified model, and show
that to obtain accurate results requires an unexpectedly extensive numerical
calculation, beyond what has been used in previous work.
