Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations

Hellmann, Frank; Kaminski, Wojciech

doi:10.48550/arxiv.1210.5276

Cited by 15 publications

(34 citation statements)

References 49 publications

(75 reference statements)

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“…At least in the k f = 0 branch, the leading contribution to the spinfoam amplitude gives a functional integration of Regge action with only small deficit angle contributions. When spin-scaling λ → ∞, only zero deficit angle mod 4πZ is allowed asymptotically, which reproduces the flatness result argued in [10].…”

supporting

confidence: 83%

“…On the other hand, the result of the analysis also connects with the recent argument about the "flatness problem" proposed in [10] when summing over spins is taken into account. In [10] the authors argue that the sum over spins in the spinfoam model may impose a projection at least in the semiclassical level, which projects out a large amount of nontrivial (semi-)classical simplicial geometry, and leaves only the geometry with deficit angle Θ f = 0 mod 4πZ.…”

supporting

confidence: 76%

“…Which has been appeared in the literature as the "flatness problem" [10]. The spinfoam state-sum in the regime λ ≥ o(γ −2 ) can be approximated by…”

Section: Re-expansion Of Euclidean and Vector Geometry Sectormentioning

confidence: 99%

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Semiclassical analysis of spinfoam model with a small Barbero-Immirzi parameter

Han

2013

Phys. Rev. D

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We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account of the sum over spins in the large spin regime. The large spin parameter λ and small Barbero-Immirzi parameter γ are treated as two independent parameters for the asymptotic expansion of spinfoam state-sum (such an idea was firstly pointed out in [11]). Interestingly, there are two different spin regimes:The model in two spin regimes has dramatically different number of effective degrees of freedom. In 1 γ −1 λ γ −2 , the model produces in the leading order a functional integration of Regge action, which gives the discrete Einstein equation for the leading contribution. There is no restriction of Lorentzian deficit angle in this regime.In the other regime λ ≥ γ −2 , only small deficit angle is allowed |Θ f | γ −1 λ 1/2 mod 4πZ. When spins go even larger, only zero deficit angle mod 4πZ is allowed asymptotically. In the transition of the two regimes, only the configurations with small deficit angle can contribute, which means one need a large triangulation in order to have oscillatory behavior of the spinfoam amplitude.

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supporting

confidence: 83%

supporting

confidence: 76%

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Semiclassical analysis of spinfoam model with a small Barbero-Immirzi parameter

Han

2013

Phys. Rev. D

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“…(1), where the deficit angle is so restricted that only Θ = 0 (flat geometry) is allowed. It relates to the "flatness problem" in spinfoam formulation discussed in [22]. However the flatness problem disappears here for any finite λ 1 by the low-energy perturbation theory [29].…”

Section: -Parameter Expansionmentioning

confidence: 99%

Covariant loop quantum gravity, low-energy perturbation theory, and Einstein gravity with high-curvature UV corrections

Han

2014

Phys. Rev. D

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A low-energy perturbation theory is developed from the nonperturbative framework of covariant loop quantum gravity (LQG) by employing the background-field method. The resulting perturbation theory is a two-parameter expansion in the semiclassical and low-energy regime. The two expansion parameters are the large spin and small curvature. The leading-order effective action coincides with the Regge action, which well approximates the Einstein-Hilbert action in the regime. The subleading corrections organized by the two expansion parameters give the modifications of the Regge action in the quantum and highenergy regime from LQG. The perturbation theory developed here shows for the first time that covariant LQG produces the high-curvature corrections to Einstein-Regge gravity. This result means that LQG is not a naive quantization of Einstein gravity; rather, it provides the UV modification. The result of the paper may be viewed as the first step toward understanding the UV completeness of LQG.The nonperturbative covariant formulation of loop quantum gravity (LQG) adapts the idea of path integral quantization to the framework of LQG [1]. In the formulation, a spinfoam amplitude AðKÞ is defined on a given simplicial manifold K for the transition of boundary quantum 3-geometries (spin-network states in LQG). 1 The spinfoam amplitude sums over the history of spin networks, and suggests a foam-like quantum spacetime structure.In this paper, a low-energy perturbation theory is developed from the nonperturbative framework of LQG. The perturbation theory explains how classical gravity emerges from the group-theoretic spinfoam formulation, and provides the high-energy (high-curvature) and quantum corrections. Here we show that an effective action can be derived after perturbatively integrating/summing over all types of spinfoam degrees of freedom fJ f ∈ IrrepðSUð2ÞÞ; g ve ∈ SLð2; CÞ; z vf ∈ CP 1 g around a geometrical background configuration. The leading-order effective action coincides with the Regge action, which well approximates the EinsteinHilbert action in the low-energy regime.Importantly, in the subleading contributions, the perturbation theory developed here shows for the first time that covariant LQG produces the high-curvature corrections to the Einstein-Regge action, which modifies the UV behavior of Einstein gravity. It is the first time that a systematic method is developed to compute the high-curvature corrections from a full LQG framework.The discussion here focuses on the Lorentzian spinfoam amplitude proposed by Engle, Pereira, Rovelli, and Livine (EPRL) [2]. The nonperturbative construction of the EPRL spinfoam amplitude is purely (quantum-)group-theoretic. As one of the representations [3], the EPRL spinfoam amplitude readsP inv e is an invariant projector onto a certain subspace of the SLð2; CÞ intertwiners associated to each tetrahedron e in K.Here f labels a triangle in K, e labels a tetrahedron, and v labels a 4-simplex. J f is the SU(2) spin assigned to each triangle. d J is the dimension of the SU(2...

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“…The situation concerning the current understanding of the dynamics of spinfoam models is comparable to that in the canonical theory. Much is known in the context of large spins, where a relation to discretised general relativity has been established [64,65] (see however [204]). On the other hand, as in the canonical theory, little is known in the context of many small spins.…”

Section: Spin Foamsmentioning

confidence: 99%

An elementary introduction to loop quantum gravity

Bodendorfer

2016

Preprint

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An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and requires only little prior knowledge of quantum mechanics, gauge theory, and general relativity. The main aim of these lectures is to provide non-experts with an elementary understanding of loop quantum gravity and to evaluate the state of the art of the field. Technical details are avoided wherever possible.

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Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations

Cited by 15 publications

References 49 publications

Semiclassical analysis of spinfoam model with a small Barbero-Immirzi parameter

Semiclassical analysis of spinfoam model with a small Barbero-Immirzi parameter

Covariant loop quantum gravity, low-energy perturbation theory, and Einstein gravity with high-curvature UV corrections

An elementary introduction to loop quantum gravity

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