Spinfoam 2d quantum gravity and discrete bundles

Abstract

In 4 dimensions, general relativity can be formulated as a constrained $BF$ theory; we show that the same is true in 2 dimensions. We describe a spinfoam quantization of this constrained BF-formulation of 2d riemannian general relativity, obtained using the Barrett-Crane technique of imposing the constraint as a restriction on the representations summed over. We obtain the expected partition function, thus providing support for the viability of the technique. The result requires the nontrivial topology of the bundle where the gravitational connection is defined, to be taken into account. For this purpose, we study the definition of a principal bundle over a simplicial base space. The model sheds light also on several other features of spinfoam quantum gravity: the reality of the partition function; the geometrical interpretation of the Newton constant, and the issue of possible finiteness of the partition function of quantum general relativity.

20 pages, 3 figures. Comments added, to appear in Class.Quant.Grav

References in corpus (12)

• Spin Foam Models for Quantum Gravity
• Relativistic spin networks and quantum gravity
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Spacetime as a Feynman diagram: the connection formulation
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• so(4) Plebanski Action and Relativistic Spin Foam Model
• Diffeomorphisms and spin foam models
• A spin foam model without bubble divergences
• Finiteness of a spinfoam model for euclidean quantum general relativity
• A left-handed simplicial action for euclidean general relativity
• Classical Euclidean general relativity from ``left-handed area = right-handed area"
• Implementing causality in the spin foam quantum geometry

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• Macroscopic observables from the comparison of local reference systems
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