THE EXACT RENORMALIZATION GROUP AND APPROXIMATE SOLUTIONS
Open accessAbstract
We investigate the structure of Polchinski’s formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff Green’s functions are given. A promising nonperturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in “irrelevancy” of operators. We illustrate with two simple models of four-dimensional λφ 4 theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.
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The simplicity constraints allow one to establish the link to LQG by restricting the group G to SU(2).
“Moreover, the constraints allow one to establish the link to LQG by restricting the group G to SU(2) [28].”
From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [28]
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Quantum Field Theory and Critical Phenomena
Zinn‐Justin, J. (2002) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780198509233.001.0001 · Cited by 5,149 · see citing works
Critical exponents from the effective average action
Tetradis, N., & WETTERICH, C. (1994) · Nuclear Physics B · doi:10.1016/0550-3213(94)90446-4 · Cited by 324 · see citing works
Critical Phenomena for Field Theorists
Weinberg, S. (1978) · Springer eBooks · doi:10.1007/978-1-4684-0931-4_1 · Cited by 190 · see citing works
Curtis, D. C., & Pennington, M. R. (1993) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.48.4933 · Cited by 54 · see citing works
Large N analysis of the Higgs mass triviality boundPreprint
Heller, U. M., Herbert Neuberger, B., & Vranas, P. M. (1992) · Cited by 16 · see citing works
Difficulties in Applying the Variational Principle to Quantum Field Theories
Feynman, R. P. (1988) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814390187_0003 · Cited by 14 · see citing works
Renormalization of Tamm-Dancoff integral equations
van de Sande, B., & Pinsky, S. S. (1992) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.46.5479 · Cited by 8 · see citing works
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Research works printed but not linked: 4
- [4][4] M. Salmhofer, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 81 -
- [5][5] M. Bonini, M. D'Attanasio and G. Marchesini, Universit` a di Parma preprint UPRF 92-360 -
- [9][9] U. Ellwanger and L. Vergara, (1992) Heidelberg preprint HD-THEP-92-49 -
- [19][19] D. Morgan, Ph.D. thesis (1991) University of Texas, Austin. -
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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
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- Authors
- MORRIS, T. R.
- Affiliations
- European Organization for Nuclear Research (CH)
- Corresponding author
- MORRIS, TIM R.
- ORCID
- MORRIS, TIM R.
- Venue
- International Journal of Modern Physics A
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1994-06-10
- Volume
- 09
- Issue
- 14
- Pages
- 2411-2449
- ISSN
- 0217-751X (ISSN-L)
- 1793-656X
- OpenAlex
- W2599891974
- Cited by
- 1,064
- References
- 7
- Citations by year
- 2026: 33 · 2025: 56 · 2024: 62 · 2023: 71 · 2022: 73 · 2021: 102 · 2020: 62 · 2019: 63 · 2018: 55 · 2017: 51 · 2016: 50 · 2015: 35 · 2014: 21 · 2013: 19 · 2012: 17
- FWCI
- 9.30
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- International Journal of Modern Physics A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- 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 › Particle physics theoretical and experimental studies
- Keywords
- exact renormalization group, phi^4 theory, renormalized coupling constant, four-dimensional field theory
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