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

Journal Article · Mon Sep 15 04:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.78.065039· OSTI ID:21254193

Baacke, Juergen ^[1]

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1. Fachbereich Physik, Universitaet Dortmund, D-44221 Dortmund (Germany)

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's 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 the 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.

• OSTI ID: 21254193
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 78; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPARATIVE EVALUATIONS
CORRECTIONS
EUCLIDEAN SPACE
FLUCTUATIONS
GREEN FUNCTION
HIGGS MODEL
INSTANTONS
MODIFICATIONS
S WAVES
SIMULATION