One-loop corrections to the instanton transition in the Abelian Higgs model: Gel’fand-Yaglom and Green’s function methods
Open accessAbstract
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.
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The ratio of functional determinants is computed using the resolvent method, developed in prior work and used in other works.
“To do so, we employ the resolvent method , developed in [24-27] and used in, e.g., [17, 28-30].”
From Double-well instantons in finite volume (2024) · cites this paper as [27]
The resolvent method states that the ratio of the determinants of two operators can be written as an integral of some modified Green's function.
“The method states that the ratio of the determinants of two operators can be written as an integral of some modified Green's function.”
From Double-well instantons in finite volume (2024) · cites this paper as [27]
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Double-well instantons in finite volume
Ai, W.-Y., Alexandre, J., Carosi, M., Garbrecht, B., & Pla, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)099 · Cited by 6 · see citing works
- Authors
- Baacke, J.
- Affiliations
- TU Dortmund University (DE)
- Corresponding author
- Baacke, Jürgen
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2008-09-25
- Volume
- 78
- Issue
- 6
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2155381545
- Cited by
- 17
- References
- 0
- Citations by year
- 2026: 1 · 2024: 3 · 2023: 2 · 2022: 1 · 2020: 2 · 2019: 1 · 2018: 2 · 2015: 2
- FWCI
- 0.53
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Abelian Higgs model, one-loop corrections, fluctuation determinant, functional determinants, pre-exponential factor
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