Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory
Open accessAbstract
We study the no-gravity limit G N → 0 of the Ponzano–Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with the Hadamard propagator) expressed as an Abelian spin foam model. We show how the G N expansion of the Ponzano–Regge amplitudes can be resummed. This leads to the conclusion that the effective dynamics of quantum particles coupled to quantum 3D gravity can be expressed in terms of an effective new non-commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators.
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BF theory with topological defects playing the role of point particles is dual, in a suitable sense, to certain non-commutative field theories in three dimensions.
“These theories have been shown by Freidel and Livine to be dual, in a suitable sense, to certain non-commutative field theories in three dimensions [185, 184].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [185]
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References 59 · Cited by 266
Research works printed but not linked: 3
- [3][3] L Freidel, D Louapre, Ponzano-Regge model revisited I: Gauge fixing observables and Lorentzian gravity , Class. Quant. Grav. 21 , 5685 (2004), hep-th/0401076. - · arXiv
- [11][11] L Freidel, D Louapre, Asymptotics of 6j and 10j symbols , Class.Quant.Grav. 20 (2003) 12671294, hep-th/0209134 - · arXiv
- [31][31] S Weinberg, Quantum Field Theory, Volume I: Foundations , Cambridge University Press (1995).
- Authors
- Freidel, L., & Livine, E. R.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Perimeter Institute (CA)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2006-03-06
- Volume
- 23
- Issue
- 6
- Pages
- 2021-2061
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1971440904
- Cited by
- 266
- References
- 59
- Citations by year
- 2026: 3 · 2025: 8 · 2024: 8 · 2023: 10 · 2022: 1 · 2021: 8 · 2020: 12 · 2019: 5 · 2018: 6 · 2017: 8 · 2016: 11 · 2015: 10 · 2014: 15 · 2013: 17 · 2012: 23
- FWCI
- 17.44
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Ponzano-Regge model, three-dimensional quantum gravity, Feynman diagrams, effective field theory, resummation, noncommutative field theory, doubly special relativity, Feynman propagator
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