Spin foam models for quantum gravity from lattice path integrals

Bonzom, Valentin

doi:10.1103/physrevd.80.064028

Cited by 79 publications

(102 citation statements)

References 45 publications

(161 reference statements)

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“…• As we see in a moment, another important role played by δ 1 is to make deficit angles ε f of emergent Regge geometries to be small but nonzero, as a resolution of the "flatness problem" in SFM [21,[43][44][45]. The detailed discussion is given momentarily below Eq.…”

Section: Spin Sum and Regularizationmentioning

confidence: 99%

“…(70) would imply strict flatness ε f = 0. This strict flatness has been proven to be one of the main obstacles for recovering classical gravity from SFMs [21,[43][44][45]. But if δ 1 is non-zero as above, then small excitations of ε f are allowed, and therefore arbitrary smooth curved geometries may emerge from refining triangulations while δ → 0.…”

Section: Equation Of Motion and Small Deficit Anglesmentioning

confidence: 99%

See 1 more Smart Citation

Emergent four-dimensional linearized gravity from a spin foam model

2019

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Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized level, classical Einstein gravity is indeed the low energy effective theory from SFMs. Thus our result heightens the confidence that covariant LQG is a consistent theory of quantum gravity. As a key technical tool, a regularization/deformation of the SFM is employed in the derivation. The deformation parameter δ becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.

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Section: Spin Sum and Regularizationmentioning

confidence: 99%

Section: Equation Of Motion and Small Deficit Anglesmentioning

confidence: 99%

Emergent four-dimensional linearized gravity from a spin foam model

2019

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“…This is close to the state-sum language, and is the usual way in which spin foam models are written down. The dual (in the sense of Fourier transform) way of describing the amplitude is given by the left hand side of (4.13), and can be interpreted as path integral for a lattice theory, with some gauge-invariant action functional determined by the S f [25,27,28], depending on finitely many holonomies. In this formulation there is a direct connection to an action functional which is determined by the S f .…”

Section: Surjective P : Bf Theorymentioning

confidence: 99%

Operator spin foam models

Bähr¹,

Hellmann²,

Kamiński³

et al. 2011

Class. Quantum Grav.

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The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as our main tool. A set of moves we define in the set of the operator spin foams allows (among other operations) to split the faces and the edges of the foams. We assign to each operator spin foam a contracted operator, by using the contractions at the vertices and suitably adjusted face amplitudes. The emergence of the face amplitudes is the consequence of assuming the invariance of the contracted operator with respect to the moves. Next, we define spin foam models and consider the class of models assumed to be symmetric with respect to the moves we have introduced, and assuming their partition functions (state sums) are defined by the contracted operators. Briefly speaking, those operator spin foam models are invariant with respect to the cellular decomposition, and are sensitive only to the topology and colouring of the foam. Imposing an extra symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with assumed invariance with respect to the edge splitting move, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on Spin(4) BF spin foam model is exactly the way we tend to view 4d quantum gravity, starting with the BC model and continuing with the EPRL or FK models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. Among our natural spin foam models there are the BF spin foam model, the BC model, and a model corresponding to the EPRL intertwiners. Our operator spin foam framework can be also used for more general spin foam models which are not symmetric with respect to one or more moves we consider.

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“…However, many questions remain unanswered. The most concerning one is the so-called flatness problem, firstly mentioned by Freidel and Conrady [24], and later explored by Bonzom [25] and Hellmann and Kaminski [26]. They argue that the EPRL partition function, in the semiclassical limit, is dominated by classical flat geometries.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

Searching for classical geometries in spin foam amplitudes: a numerical method

Donà

Gozzini

Sarno

2020

Class. Quantum Grav.

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We develop a numerical method to investigate the semiclassical limit of spin foam amplitudes with many vertices. We test it using the Ponzano-Regge model, a spin foam model for three-dimensional euclidean gravity, and a transition amplitude with three vertices. We study the summation over bulk spins, and we identify the stationary phase points that dominate it and that correspond to classical geometries. We complement with the numerical analysis of a four vertex transition amplitude and with a modification of the model that includes local curvature. We discuss the generalization of our results to the four-dimensional EPRL spin foam model, and we provide suggestions for new computations.

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Spin foam models for quantum gravity from lattice path integrals

Cited by 79 publications

References 45 publications

Emergent four-dimensional linearized gravity from a spin foam model

Emergent four-dimensional linearized gravity from a spin foam model

Operator spin foam models

Searching for classical geometries in spin foam amplitudes: a numerical method

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