One-loop corrections to the instanton transition in the Abelian Higgs model: Gel'fand-Yaglom and Green's function methods

Abstract

The fluctuation determinant, the preexponential factor for the instanton transition, has been computed several years ago in the Abelian Higgs model, using a method based on integrating the Euclidean Green' function. A more elegant method for computing functional determinants, using the Gel'fand-Yaglom theorem, has been applied recently to a variety of systems. This method runs into difficulties if the background field has nontrivial topology, as is the case for the instanton in the Abelian Higgs model. A shift in thre effective centrifugal barriers makes the s-wave contribution infinite, an infinity that is compensated by the summation over the other partial waves. This requires some modifications of the Gel'fand-Yaglom method which are the main subject of this work. We present here both, the Green' s function and the Gel'fand-Yaglom method and compare the numerical results in detail.

arXiv comment34 pages, 5 figures

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Cited by in corpus (15)

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• Radiative effects on false vacuum decay in Higgs-Yukawa theory
• Gradient effects on false vacuum decay in gauge theory
• False vacuum decay rates, more precisely
• Spectral Methods for Coupled Channels with a Mass Gap
• Double-well instantons in finite volume
• Vacuum polarization energy of a complex scalar field in a vortex background
• Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator
• One-loop corrections to the Nielsen-Olesen vortex: collective oscillations
• Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls
• On equivalent methods for functional determinants