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.

arXiv comment14 pages, 8 figures,v2: typos corrected, v3: figure 2 updated

References in corpus (15)

• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Energy, Central Charge, and the BPS Bound for 1+1 Dimensional Supersymmetric Solitons
• Light Nuclei as Quantized Skyrmions
• Vacuum energy in a spherically symmetric background field
• Quantum Energies of Interfaces
• Quantum QED Flux Tubes in 2+1 and 3+1 Dimensions
• Quantum Aspects of Supersymmetric Maxwell Chern-Simons Solitons
• Renormalization of the Abelian-Higgs Model in the R-xi and Unitary gauges and the physicality of its scalar potential
• 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
• Fermion-induced effective action in the presence of a static inhomogeneous magnetic field
• Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts
• Erratum: One-loop corrections to the string tension of the vortex in the Abelian Higgs model
• One-loop corrections to the string tension of the vortex in the Abelian Higgs model
• 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 $D=3+1$