Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space

Pietri, R. De; Freidel, Laurent; Krasnov, Kirill; Rovelli, Carlo

doi:10.1016/s0550-3213(00)00005-5

Cited by 207 publications

(394 citation statements)

References 41 publications

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“…This seems to severely limit the physical relevance of such proposals. Model B in [35] is the only normalization of the Barrett-Crane model which satisfies the minimal requirements of background independence presented here and is the one naturally arising in the quantization of Plebanski's Spin(4) formulation of gravity presented in [4]. However, a non trivial modification of the edge amplitude for generic edges should appear due to the contribution of the simplicity constraints as argued in Section 3.…”

Section: Discussionmentioning

confidence: 84%

“…In particular, without modification of the singular edge amplitude (associated with edges bounded by less than four faces), the finite normalizations for both the Riemannian and Lorentzian Barrett-Crane model proposed in [20,34] are to be regarded as formulations where the diffeomorphism gauge symmetry has been broken by an anomalous path integral measure. † Other anomalous formulations are: the new normalization of the Barrett-Crane model proposed in [18] to improve the convergence properties of the previous model and Model A in [35]. This seems to severely limit the physical relevance of such proposals.…”

Section: Discussionmentioning

confidence: 99%

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Spin foam quantization and anomalies

Bojowald

Pérez

2009

Gen Relativ Gravit

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Abstract. The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain-Kuchař model.

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Section: Discussionmentioning

confidence: 84%

Section: Discussionmentioning

confidence: 99%

Spin foam quantization and anomalies

Bojowald

Pérez

2009

Gen Relativ Gravit

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“…This structure was calling a field theory interpretation of spin foam models. It was eventually found in [25] that the Barrett-Crane spin foam model can remarkably be interpreted as a Feynman graph of a new type of theory baptized 'group field theory' (GFT for short). The GFT structure was first discovered by Boulatov [26] in the context of three dimensional gravity where a similar connection was made and further developed by Ooguri in the context of 4d BF theory [10].…”

Section: Introductionmentioning

confidence: 99%

Group Field Theory: An Overview

2005

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We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that this theory leads to a natural proposal for the physical scalar product of quantum gravity. We also show in which sense this theory provides a third quantization point of view on quantum gravity.

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“…One proposal for performing such a sum is that of a generating field theory [21,13,16,22]. This is usually a field theory on the gauge group which generates discretized space-times as its Feynman diagrams.…”

Section: Discussionmentioning

confidence: 99%

“…While different versions of the Euclidean Barrett-Crane model have been proposed [16,17,18,19,20] we consider a version which appears to be the most natural one in our framework. For ease of terminology we refer to it in the following as "the" Barrett-Crane model.…”

Section: The Barrett-crane Modelmentioning

confidence: 99%

Renormalization of discrete models without background

Oeckl

2003

Nuclear Physics B

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Conventional renormalization methods in statistical physics and lattice quantum field theory assume a flat metric background. We outline here a generalization of such methods to models on discretized spaces without metric background. Cellular decompositions play the role of discretizations. The group of scale transformations is replaced by the groupoid of changes of cellular decompositions. We introduce cellular moves which generate this groupoid and allow to define a renormalization groupoid flow.We proceed to test our approach on several models. Quantum BF theory is the simplest example as it is almost topological and the renormalization almost trivial. More interesting is generalized lattice gauge theory for which a qualitative picture of the renormalization groupoid flow can be given. This is confirmed by the exact renormalization in dimension two.A main motivation for our approach are discrete models of quantum gravity. We investigate both the Reisenberger and the Barrett-Crane spin foam model in view of their amenability to a renormalization treatment. In the second case a lack of tunable local parameters prompts us to introduce a new model. For the Reisenberger and the new model we discuss qualitative aspects of the renormalization groupoid flow. In both cases quantum BF theory is the UV fixed point. *

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Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space

Cited by 207 publications

References 41 publications

Spin foam quantization and anomalies

Spin foam quantization and anomalies

Group Field Theory: An Overview

Renormalization of discrete models without background

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