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'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.