Butterfield: question on spin foam cosmology, about relaxing the various approximations and about obtaining more genaral anisotropic geometries. Vidotto: one can indeed generalize the class of states used, and use them to study anisotropic situations. A more difficult question is the dynamical one, i.e. relaxing the approximation to the dynamics that are used. But results are encouraging.

Conclusions: highlight two main open issues. One: dynamical – what physical processes lead to decoherence in this context. Two: conceptual – do spin foams resolve the problem of time?

Application of general idea to the setting of “spin foam cosmology”, where results are available about obtaining semi-classicality in the spin foam setting. Lots of unsettled questions but interesting results to consider. Brief summary of framework and of approximations used.

Can write down formaly the decoherence functional in terms of the sum over 2-complexes, which is however very difficult to control. Still, one can at least identify which properties such functional should satisfy.

Comment by Dittrich: these observables are not diffeo-invariant, however. Indeed, an interesting issue, says the speaker.

The interesting and important question is to identify the quantities in terms of which one defines the coarse graining. One choice is to look at intrinsic and extrinsic curvature [as in the definition of coherent states], another is to look at volume operator [it has been considered in the loop quantum cosmology context].

Move on to the definition of the decoherence functional in this context. Fine-grained histories of spin networks are the individual spin foams, weighted by the “fundamental” spin foam amplitudes that the theory associated to them. Coarse graining is imposed on “bulk configurations”, that is on the spin foams being summed over. More precisely, one coarse grains all histories/spin foams that correspond to the same diff-invariant properties [identified in terms of suitable observables].

notion of coherent states as semiclassical states peaking on the classical phase space variables associated to a given graph [no superposition of graphs considered, here]

Summary of the dynamics: analog of path integral [sum-over-histories] is sum over all 2-complexes and sum over colorings, weighted by quantum amplitude.