Functional methods and perturbation theory
Abstract
The framework of functional integrals in field theory is convenient for presenting a unified view of the perturbation expansion according to the number of loops. We review the calculation of the generating functional for irreducible Green functions and its renormalization properties. Calculations of the effective potential and $Z$-function are carried up to the order of two loops for the self-coupled scalar field. This is applied to compute the coefficients of the Callan-Symanzik equation which describes the short distance behavior of the theory. In conclusion, we present some speculations concerning the positivity of the coupling constant, and its relation to the on -shell two-particle scattering amplitude.
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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 [4]
Cites
On gauge invariance and vacuum polarization
Schwinger, J. (1951) · Physical Review · doi:10.1103/physrev.82.664 · Cited by 7,116 · see citing works
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Non-perturbative renormalization flow in quantum field theory and statistical physics
Berges, J., Tetradis, N., & Wetterich, C. (2002) · Physics Reports · doi:10.1016/s0370-1573(01)00098-9 · Cited by 1,548 · see citing works
Convexity, gauge-dependence and tunneling rates
Plascencia, A. D., & Tamarit, C. (2016) · Journal of High Energy Physics · doi:10.1007/jhep10(2016)099 · Cited by 64 · see citing works
Spinodal decomposition in quantum field theory
Calzetta, E. (1989) · Annals of Physics · doi:10.1016/0003-4916(89)90260-1 · Cited by 38 · see citing works
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
- Iliopoulos, J., Itzykson, C., & Martin, A.
- Affiliations
- Laboratoire de Physique Théorique et Hautes Energies (FR)
- ORCID
- Martin, A.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1975-01-01
- Volume
- 47
- Issue
- 1
- Pages
- 165-192
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W1973787974
- Cited by
- 401
- References
- 1
- Citations by year
- 2026: 3 · 2025: 16 · 2024: 9 · 2023: 9 · 2022: 11 · 2021: 7 · 2020: 24 · 2019: 7 · 2018: 5 · 2017: 5 · 2016: 4 · 2015: 5 · 2014: 1 · 2013: 7 · 2012: 5
- FWCI
- 9.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Reviews of Modern Physics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- 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 › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- functional methods, perturbation theory, generating functional, renormalization, effective potential, Callan-Symanzik equation, two-loop calculations, loop expansion
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