Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude

Barrett, John W.; Dowdall, Richard J.; Fairbairn, Winston J.; Gomes, Henrique; Hellmann, Frank

doi:10.1063/1.3244218

Cited by 181 publications

(306 citation statements)

References 30 publications

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“…(D9) 16 The construction of critical solutions from arbitrary Regge geometries can be done locally in each 4-simplex as explained in [44], see also [25] in Lorentzian signature. 17 One should also take into account the gauge invariance g ± ve → κ ve g ± ve (κ ve = ±1) of spinfoam action, which removes some lift ambiguities.…”

Section: Appendix A: Spin Sum In Spinfoam Amplitudementioning

confidence: 99%

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Han

2017

Phys. Rev. D

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In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of Einstein equation can be approached by dominant configurations in spinfoam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spinfoam formulation, and how to take advantage of it.

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Section: Appendix A: Spin Sum In Spinfoam Amplitudementioning

confidence: 99%

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Han

2017

Phys. Rev. D

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“…This renormalizable trace is just the multiple integral over SL(2, C) [3,4], which played a crucial role in the finiteness of the BC model, and goes over to the new model. The renormalization just consists in dropping one of the integrations (it doesnt matter which).…”

Section: The Time Functormentioning

confidence: 99%

“…We would like to see classical general relativity emerge for distance scales above the Planck length. It was shown in [4] that classical geometry dominates the integral expression corresponding to a classical four simplex in the limit of large spins. However there is nothing in the model corresponding to larger composite "coarse grained" simplices, and no reason to associate higher spins to them.…”

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confidence: 99%

Holography in the EPRL Model

Crane¹

2012

Found Phys

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In this research announcement, we propose a new interpretation of the EPR quantization of the BC model using a functor we call the time functor, which is the first example of a CLa-ren functor. Under the hypothesis that the universe is in the Kodama state, we construct a holographic version of the model. Generalisations to other CLa-ren functors and connections to model category theory are considered.Comment: research announcement. Latex fil

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“…The asymptotic geometry of the one-vertex decomposable amplitude is given by the asymptotic analysis in Refs. [13,[37][38][39]. It consists of two distinct flat 4-simplices with uncorrelated geometry.…”

Section: A the 4-simplex Graphmentioning

confidence: 99%

Expansions in spin foam cosmology

Hellmann

2011

Phys. Rev. D

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We discuss the expansions used in spin foam cosmology. We point out that already at the one-vertex level, arbitrarily complicated amplitudes contribute and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expansion. We show that the factorization of the amplitude originally considered is best interpreted in topological terms. We then consider the next-higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector and conclude that it is necessary to truncate the dynamics as well.

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Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude

Cited by 181 publications

References 30 publications

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Holography in the EPRL Model

Expansions in spin foam cosmology

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