Vacuum polarization energy of a complex scalar field in a vortex background

TL;DR

This paper develops a gauge-invariant scattering method to compute the quantum vacuum polarization energy of a vortex in a U(1) Higgs-gauge theory, revealing the need for extensive numerical calculations for accurate results.

Contribution

It introduces modifications to standard scattering techniques to preserve gauge invariance in vortex energy calculations.

Findings

Gauge-invariant scattering approach is feasible for vortex energy.

Accurate results require extensive numerical computation.

Standard methods need adjustments to handle topological singularities.

Abstract

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.