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arXiv · 1910.09348

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

N. Graham·H. Weigel
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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.

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N. Graham, H. Weigel. 2019-10-21. Vacuum polarization energy of a complex scalar field in a vortex background. https://doi.org/10.1103/physrevd.101.076006

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