Paper detail

Bubble divergences and gauge symmetries in spin foams

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.