Asymptotics of loop quantum gravity fusion coefficients
Open accessAbstract
The fusion coefficients from SO (3) to SO (4) play a key role in the definition of spin foam models for the dynamics in loop quantum gravity. In this paper we give a simple analytic formula of the Engle–Pereira–Rovelli–Livine fusion coefficients. We study the large spin asymptotics and show that they map SO (3) semiclassical intertwiners into SU (2) L × SU (2) R semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.
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The Warsaw modification does not affect the leading-order results of the semiclassical limit.
“Notice that this modification does not interfere with the results of the semiclassical limit (to leading order) as reviewed in Section 13.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [1]
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“…= P j ψ(j)〈W |E a n·E b nE c m·E d m|j,Φ(~n)〉 P j ψ(j)〈W |j,Φ(~n)〉 − P j ψ(j)〈W |E a n·E b n|j,Φ(~n)〉 P j ψ(j)〈W |j,Φ(~n)〉 P j ψ(j)〈W |E c m·E d m|j,Φ(~n)〉 P j ψ(j)〈W |j,Φ(~n)〉 (36) In the following two subsections we recall the integral formula for the amplitude of a coherent spin network 〈W…”
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- Authors
- Alesci, E., Bianchi, E., Magliaro, E., & Perini, C.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Roma Tre University (IT)
- ORCID
- Alesci, Emanuele
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2010-03-26
- Volume
- 27
- Issue
- 9
- Pages
- 095016
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2043289540
- Cited by
- 15
- References
- 41
- Citations by year
- 2013: 1 · 2012: 2
- FWCI
- 2.50
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- HAL (submittedVersion, other-oa)
- SDL (submittedVersion)
- Trinity's Access to Research Output (TARA) (Trinity College Dublin) (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
- loop quantum gravity, spin foam models, fusion coefficients, EPRL model, analytic formula
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