Bubble divergences and gauge symmetries in spin foams

Abstract

Spin foams are candidate state-sum models for transition amplitudes in quantum gravity. An active research subject is to identify the possible divergences of spin foam models, or alternatively to show that models are finite. We will discuss in detail the (non--occurrence of) divergences in the Barrett-Crane model, formulated as an integral of delta function weights only. We will furthermore present a simple method to estimate the divergence degree of the so-called bubbles for general spin foam models. Divergences in spin foams are expected to be related to the existence of gauge symmetries (diffeomorphisms). Thus we have to conclude that such gauge symmetries are not (fully) present in the model we consider. But we will identify a class of gauge symmetries which occur at special solutions of the equations imposed by the delta function weights. This situation is surprisingly similar to the case of broken diffeomorphism symmetries in discrete gravity, which are present around flat solutions. We introduce a method to derive (Ward-identity-like) equations for the vertex amplitude of the model in the case of broken gauge symmetries.

28 pages

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• Quantum group spin nets: refinement limit and relation to spin foams
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Dirac's discrete hypersurface deformation algebras
• An elementary introduction to loop quantum gravity
• Towards a Cosmological subsector of Spin Foam Quantum Gravity
• From spin foams to area metric dynamics to gravitons
• Quantization of systems with temporally varying discretization II: Local evolution moves
• Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
• Bulk amplitude and degree of divergence in 4d spin foams
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• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Tullio Regge's legacy: Regge calculus and discrete gravity
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• The Barrett-Crane model: asymptotic measure factor
• The Ponzano-Regge cylinder and Propagator for 3d quantum gravity
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