Visualising quantum effective action calculations in zero dimensions
Open accessAbstract
We present an explicit treatment of the two-particle-irreducible (2PI) effective action for a zero-dimensional quantum field theory. The advantage of this simple playground is that we are required to deal only with functions rather than functionals, making complete analytic approximations accessible and full numerical evaluation of the exact result possible. Moreover, it permits us to plot intuitive graphical representations of the behaviour of the effective action, as well as the objects out of which it is built. We illustrate the subtleties of the behaviour of the sources and their convex-conjugate variables, and their relation to the various saddle points of the path integral. With this understood, we describe the convexity of the 2PI effective action and provide a comprehensive explanation of how the Maxwell construction arises in the case of multiple, classically stable saddle points, finding results that are consistent with previous studies of the one-particle-irreducible (1PI) effective action.
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Tunnelling between degenerate vacua is at the origin of convexity of the effective potential and restoration of a symmetric true vacuum.
“while the second is at the origin of convexity of the effective potential [2-11] and therefore restoration of a symmetric true vacuum.”
From Double-well instantons in finite volume (2024) · cites this paper as [11]
Section 6, “Multiple saddle points and the Maxwell construction” (page unavailable), shows that contributions from two minima produce a flat effective potential between symmetric minima in the zero-dimensional model. The paper supports the connection between competing vacua and convexity, but does not identify tunnelling as its cause or explicitly establish restoration of a symmetric true vacuum. (LLM, conf=0.82)
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Research works printed but not linked: 27
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Cited by
Sorted by citations
Symmetry restoration, tunneling, and the null energy condition
Alexandre, J., & Polonyi, J. (2022) · Physical Review D · doi:10.1103/physrevd.106.065008 · Cited by 8 · see citing works
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
- Millington, P., & Saffin, P. M.
- Affiliations
- University of Nottingham (GB)
- Venue
- Journal of Physics A: Mathematical and Theoretical
- Publisher
- IOP Publishing
- Published
- 2019-09-12
- Volume
- 52
- Issue
- 40
- Pages
- 405401
- ISSN
- 1751-8113 (ISSN-L)
- 1751-8121
- OpenAlex
- W2945223376
- Cited by
- 23
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 3 · 2023: 3 · 2022: 9 · 2021: 4 · 2020: 1 · 2019: 1
- FWCI
- 2.19
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of Physics A Mathematical and Theoretical (publishedVersion, cc-by)
- Repository@Nottingham (University of Nottingham) (publishedVersion, cc-by)
- arXiv (Cornell University) (acceptedVersion)
- Repository@Nottingham (University of Nottingham) (submittedVersion, cc-by)
- Research Explorer (The University of Manchester) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Science and Technology Facilities Council (ST/L000393/1)
- Leverhulme Trust
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Physical Sciences › Mathematics › Mathematical Physics › advanced mathematical theories
- Keywords
- two-particle irreducible effective action, Maxwell construction, saddle points
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