Functional evaluation of the effective potential
Abstract
By use of the path-integral formulation of quantum mechanics, a series expansion for the effective potential is derived. Each order of the series corresponds to an infinite set of conventional Feynman diagrams, with a fixed number of loops. As an application of the formalism, three calculations are performed. For a set of $n$ self-interacting scalar fields, the effective potential is computed to the two-loop approximation. Also, all loops are summed in the leading-logarithmic approximation when $n$ gets large. Finally, the effective potential for scalar, massless electrodynamics is derived in an arbitrary gauge. It is found that the potential is gauge-dependent, and a specific gauge is exhibited in which all one-loop effects disappear.
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This quantity can be identified as the one-loop correction to the 1PI effective action around the kink configuration, having subtracted the correction around the static one.
“We can identify this quantity as the one-loop correction to the 1PI effective action [32] around the kink configuration, having subtracted the correction around the static one.”
From Double-well instantons in finite volume (2024) · cites this paper as [32]
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Calzetta, E. (1989) · Annals of Physics · doi:10.1016/0003-4916(89)90260-1 · Cited by 38 · 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
- Jackiw, R.
- Affiliations
- Massachusetts Institute of Technology (US)
- Corresponding author
- Jackiw, R.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1974-03-15
- Volume
- 9
- Issue
- 6
- Pages
- 1686-1701
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2034929369
- Cited by
- 901
- References
- 0
- Citations by year
- 2026: 18 · 2025: 30 · 2024: 36 · 2023: 30 · 2022: 25 · 2021: 30 · 2020: 44 · 2019: 20 · 2018: 20 · 2017: 13 · 2016: 27 · 2015: 21 · 2014: 17 · 2013: 21 · 2012: 15
- FWCI
- 16.24
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Keywords
- effective potential, path integral, series expansion, Feynman diagrams, two-loop approximation, 1/N expansion, leading logarithmic approximation, self-interacting scalar field, gauge dependence, quantum field theory
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