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Cited by 43Particle physics theoretical and experimental studiesCosmology and Gravitation TheoriesBlack Holes and Theoretical Physics

Green’s function method for handling radiative effects on false vacuum decay

Open access
Garbrecht, Björn, Millington, Peter·2015·Physical Review D
DOI 10.1103/physrevd.91.105021
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Abstract

We introduce a Green's function method for handling radiative effects on false vacuum decay. In addition to the usual thin-wall approximation, we achieve further simplification by treating the bubble wall in the planar limit. As an application, we take the $\ensuremath{\lambda}{\mathrm{\ensuremath{\Phi}}}^{4}$ theory, extended with $N$ additional heavier scalars, wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself.

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  • The solution for the τ-dependent part of the modified Green's function around the instanton can be obtained in terms of associated Legendre functions P_{μ_n/2}(u) and Q_{μ_n/2}(u).

    “The solution to the equation above can be obtained in terms of associated Legendre functions P µ n 2 ( u ) and Q µ n 2 ( u ) [17, 31]. It reads [28]”

    From Double-well instantons in finite volume (2024) · cites this paper as [28]

    Section III (p. 5) says the Green’s-function equation has solutions expressible in associated Legendre functions. Appendix B, §3 (p. 13) identifies first- and second-kind functions P and Q, but the available text does not establish the specific index μ_n/2 attributed to this source. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • 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 [28]

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Cited by

Sorted by citations

Authors
Garbrecht, B., & Millington, P.
Affiliations
Technical University of Munich (DE)
ORCID
Millington, Peter
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2015-05-26
Volume
91
Issue
10
ISSN
  • 0556-2821 (ISSN-L)
  • 1550-7998
  • 1550-2368
DOI
10.1103/physrevd.91.105021
OpenAlex
W1575804873
Cited by
43
References
4
Citations by year
2026: 2 · 2025: 3 · 2024: 4 · 2023: 4 · 2022: 4 · 2021: 1 · 2020: 3 · 2019: 4 · 2018: 5 · 2017: 5 · 2016: 7 · 2015: 1
FWCI
3.01
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • arXiv (Cornell University) (acceptedVersion)
  • Research Explorer (The University of Manchester) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Technische Universität München
  • Deutsche Forschungsgemeinschaft
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
false vacuum decay, radiative corrections, Green's function method, thin-wall approximation, planar limit, bubble walls, phi^4 theory, scalar field theory, functional determinants

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