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.
Highlights
Topological vortex configurations appear in many field theory models in the form of axially symmetric U(1) vector potentials pointing in azimuthal direction
1Department of Physics, Middlebury College Middlebury, Vermont 05753, USA 2Institute for Theoretical Physics, Physics Department, Stellenbosch University, Matieland 7602, South Africa (Received 4 February 2020; accepted 17 March 2020; published 7 April 2020). Scattering methods make it possible to compute the effects of renormalized quantum fluctuations on classical field configurations
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
Summary
Topological vortex configurations appear in many field theory models in the form of axially symmetric U(1) vector potentials pointing in azimuthal direction. Physically measurable quantities remain well defined, in these models the field profiles, which depend on the gauge choice, necessarily have a singular structure This structure hampers many computations that go beyond the (static) mean-field approach, the quantum correction to the classical static energy density per unit length. Calculations of the VPE often use auxiliary quantities like Feynman diagrams and/or expansion schemes for scattering data [1] These quantities are not necessarily gauge invariant and the singular structure matters. The quantum fluctuations propagate in a combined potential generated by both the gauge and scalar field backgrounds The latter provides the dominant contribution, but the correct identification and renormalization of the ultraviolet divergences requires a detailed analysis of the interaction with the vortex background. × ηlðρÞ 1⁄4 0; ð5Þ with the dispersion relation ω2 1⁄4 k2 þ m2 and the abbreviation
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