Semiclassical limit of 4-dimensional spin foam models
Open accessAbstract
We study the semiclassical properties of the Riemannian spin foam models with Immirzi parameter that are constructed via coherent states. We show that, in the semiclassical limit, the quantum spin foam amplitudes of an arbitrary triangulation are exponentially suppressed if the face spins do not correspond to a discrete geometry. When they do arise from a geometry, the amplitudes reduce to the exponential of $\mathrm{i}$ times the Regge action. Remarkably, the dependence on the Immirzi parameter disappears in this limit.
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For geometric configurations, the amplitude asymptotics receives contributions from both degenerate and non-degenerate configurations.
“If configurations are geometric (i.e., Regge-like) one has two kinds of contributions to the amplitude asymptotics: those coming from degenerate and non-degenerate configurations.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [122]
Non-geometric solutions of the equations of motion of the effective discrete action are not critical and are exponentially suppressed in the scaling jf → λjf with λ ≫ 1.
“They show that those solutions of the equations of motion of the effective discrete action that are non-geometric (i.e., the opposite of Regge-like) are not critical and hence exponentially suppressed in the scaling jf → λjf with λ ≫ 1.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [122]
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- Authors
- Conrady, F., & Freidel, L.
- Affiliations
- Perimeter Institute (CA)
- ORCID
- Freidel, Laurent
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2008-11-19
- Volume
- 78
- Issue
- 10
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2144537392
- Cited by
- 213
- References
- 55
- Citations by year
- 2025: 2 · 2024: 8 · 2023: 9 · 2022: 5 · 2021: 9 · 2020: 11 · 2019: 9 · 2018: 10 · 2017: 12 · 2016: 12 · 2015: 6 · 2014: 10 · 2013: 20 · 2012: 22
- FWCI
- 17.34
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- semiclassical limit, spin foam models, Immirzi parameter, coherent states, quantum gravity, Regge action, triangulation, combinatorial geometry
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