Move on to the covariant formulation of loop quantum gravity, that is to the spin foam formalism. Brief summary of the kinematical states of the theory [cylindrical functions and spin networks, as in lattice gauge theory]. Summary of the covariant definition of the dynamics: spin foams as histories of spin networks, defined by 2-complexes with the same type of coloring as spin network states. 

More on the properties of the decoherence functional. Generalization of these concepts and definitions to the field theory [formulated in terms of path integrals] context and to GR [in particular in its Hamiltonian formulation].

More detailed definition of partition and coarse-graining of histories in this example. definition of class operator and decoherence functional for the histories. identification of the [decoherence] conditions that are necessary to be able to assign probabilities to the histories [basically amounting exactly to the suppression of interference between histories).

Summary of idea of sum over histories as a way to describe in a covariant way the dynamics of a quantum system. Example of the [fine-grained] histories of a single particle and basic notion of coarse graining of such histories.

One motivation to use decoherence is that this Copenhagen story is questionable in many ways. One more motivation is that in the general relativistic context, no time variable can be used to describe when the collapse happens, and a covariant version of the suppression of superposition and interference should be looked for.

In the Copenhagen interpretation, this interference is suppressed by measurement, via instantaneous “collapse” of the wave function to a given state.

general introduction to decoherence, in the context of closed quantum systems. Stress the difference with the classical situation in which a single history of the system is realized and is selected by the theory. It is difficult to assign probabilities to histories, in the quantum case, because of interference, mathematically the fact that we work with probabilities amplitudes for states and histories, and not probabilities themselves.

More on decoherence; focus on the histories of spin networks , that is spin foams. Main point: how to assign probabilities to such histories. Importance of decoherence in providing these quantities.

Butterfield: superselection is actually the more general concept and mechanism to be studied, decoherence being one particular way in which such superselection is achieved by coupling with the environment. Speaker agrees, but stresses how this point of view rests to some extent on the general attitute towards quantum mechanics and its relation with the classical world.

Comment by Butterfield: importance of superselection in achieving classicality.