Complete LQG propagator. II. Asymptotic behavior of the vertex
Open accessAbstract
In a previous article we have shown that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit.
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The Barrett-Crane two-point function could not yield the expected result compatible with Regge gravity in the semiclassical limit.
“It was then applied to the Barrett-Crane model in [5, 4, 77], where it was discovered that certain components of the two-point function could not yield the expected result compatible with Regge gravity in the semiclassical limit.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [5]
The Barrett-Crane model's failure to give the correct propagator scaling can be traced back to a missing coherent cancellation of phases between the intertwiner wave function of the semiclassical boundary state and the intertwiner dependence of the model.
“The problem can be traced back to a missing coherent cancellation of phases between the intertwiner wave function of the semiclassical boundary state and the intertwiner dependence of the model.”
From LQG propagator from the new spin foams (2009) · cites this paper as [13]
The Barrett-Crane spin foam model fails to give the correct scaling behavior for off-diagonal components of the graviton propagator.
“The analysis of [12,13] shows that the Barrett-Crane model fails to give the correct scaling behavior for off-diagonal components of the graviton propagator.”
From LQG propagator from the new spin foams (2009) · cites this paper as [13]
The off-diagonal components are not suppressed as happened for the Barrett-Crane model [12,13] and have the same scaling as the diagonal ones.
“The off-diagonal components are not suppressed as happened for the Barrett-Crane model [12,13] and have the same scaling as the diagonal ones.”
From LQG propagator from the new spin foams (2009) · cites this paper as [13]
In the recoupling basis for intertwiner space, the off-diagonal components of the metric operator generally have non-trivial matrix elements.
“Using the recoupling basis for intertwiner space, we have that in general the off-diagonal components of the metric operator have non-trivial matrix elements”
From LQG propagator from the new spin foams (2009) · cites this paper as [13]
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References 61 · Cited by 89
Research works printed but not linked: 5
- [1][1] L. Modesto, C. Rovelli, 'Particle scattering in loop quantum gravity', Phys. Rev. Lett. 95 (2005), 191301. C. Rovelli, 'Graviton propagator from background-independent quantum gravity', Phys.Rev. Lett. 97 (2006), 151301. -
- [2][2] E.Bianchi, L. Modesto, C. Rovelli, S. Speziale, 'Graviton propagator in loop quantum gravity', Class. Quant. Grav. 23 (2006), 6989-7028. -
- [4][4] E.Alesci, C. Rovelli, 'The complete LQG graviton propagator: I. Difficulties with the BarrettCrane vertex', Phys. Rev. D, to appear (2007), arXiv:07080883. -
- [14][14] E.Magliaro, C. Perini, C. Rovelli: 'Compatibility of radial, Lorenz and harmonic gauges', Phys. Rev. D, to appear, arXiv:0704.0992. - · arXiv
- [18][18] E.Magliaro, C. Perini, C. Rovelli, 'Numerical indications on the semiclassical limit of the flipped vertex', arXiv:0710.5034. · arXiv
- Authors
- Alesci, E., & Rovelli, C.
- Affiliations
- Roma Tre University (IT)
- ORCID
- Alesci, Emanuele
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2008-02-14
- Volume
- 77
- Issue
- 4
- Pages
- 044024
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2100445593
- Cited by
- 89
- References
- 61
- Citations by year
- 2024: 1 · 2022: 1 · 2021: 1 · 2020: 2 · 2019: 4 · 2018: 2 · 2017: 4 · 2016: 3 · 2015: 2 · 2014: 5 · 2013: 7 · 2012: 8
- FWCI
- 12.11
- 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)
- HAL (submittedVersion, other-oa)
- SDL (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, graviton propagator, vertex amplitude, intertwiners, asymptotic behavior, quantum gravity
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