Spin foam models: the dynamics of quantum geometry

Abstract

In this paper, we give an overview of the main techniques developed in the context of background independent gravity in order to tackle the problem of the dynamics. We briefly introduce loop quantum gravity, highlighting some of its achievements and then present spin foam models which allows the construction of dynamical transition amplitudes between loop quantum gravity states. We then present three types of applications of these sets of ideas. First, we describe how the coupling to matter can be achieved in this context and how this has allowed us to show that in 2+1 the effective geometry created by quantum gravity is non-commutative. Then we present how we can extract information of the graviton propagator from spin foam amplitudes and finally we emphasize some recent application to quantum cosmology.