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

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.

14 pages, 8 figures,v2: typos corrected, v3: figure 2 updated

References in corpus (4)

• Light Nuclei as Quantized Skyrmions
• One-loop corrections to the instanton transition in the Abelian Higgs model: Gel'fand-Yaglom and Green's function methods
• Fermion Energies in the Background of a Cosmic String
• Quantum corrections to vortex masses and energies

Cited by in corpus (3)

• Quantum Corrections to Soliton Energies
• Winding number dependence of quantum vortex energies at one-loop
• Quantum energies of BPS vortices in $D=2+1$ and $D=3+1$