Dual variables and a connection picture for the Euclidean Barrett–Crane model

Pfeiffer, Hendryk

doi:10.1088/0264-9381/19/6/306

Cited by 19 publications

(66 citation statements)

References 29 publications

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“…There is another formula to define the volume, which can be seen as more suitable in our framework in which 1 The reconstruction of a (discrete) connection or parallel transport from the two normals associated to each tetrahedron was also discussed in [20] in the context of the Euclidean Barrett-Crane model.…”

Section: Geometric Meaning Of the Variables Of The Modelmentioning

confidence: 99%

Implementing causality in the spin foam quantum geometry

2003

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We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantum gravity states, i.e. realising in the spin foam context the Feynman propagator between states. The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order Regge calculus, and represents a link between several approaches to quantum gravity as canonical loop quantum gravity, sum-over-histories formulations, dynamical triangulations and causal sets. In particular, we show how the resulting model can be rephrased within the framework of quantum causal sets (or histories).2

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Section: Geometric Meaning Of the Variables Of The Modelmentioning

confidence: 99%

Implementing causality in the spin foam quantum geometry

2003

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“…Our treatment in the following directly applies to general cellular decompositions. It is closely related to the connection formulation of which an extensive treatment can be found in [19].…”

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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“…Several variations of the model have been studied [1,8,19] which differ in their tetrahedron amplitudes, obtained either from ideas of lattice gauge theory [13,14,15] or from particularly simple actions in the formulation as a field theory on a group [8,19] (note that papers written in the language of a field theory on a group use the two-complex dual to the triangulation).…”

Section: The Barrett-crane Modelmentioning

confidence: 99%

Spin foam model for pure gauge theory coupled to quantum gravity

Oriti

Pfeiffer

2002

Phys. Rev. D

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We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a fourmanifold which is given merely combinatorially. The Riemannian Barrett-Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang-Mills action. The model is designed so that one obtains a continuum approximation of the gauge theory sector at an effective level, similarly to the continuum limit of lattice gauge theory, when the typical length scale of gravity is much smaller than the Yang-Mills scale.

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Dual variables and a connection picture for the Euclidean Barrett–Crane model

Cited by 19 publications

References 29 publications

Implementing causality in the spin foam quantum geometry

Implementing causality in the spin foam quantum geometry

Renormalization of discrete models without background

Spin foam model for pure gauge theory coupled to quantum gravity

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