Transition amplitudes in non-simplicial spin foams

2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions

We compute transition amplitudes between two spin networks with dipolegraphs, using the lorentzian eprl model with up to two (non-simplicial)vertices.We find power-law decreasing amplitudes in the large spin limit, decreasing faster as the complexity of the foam increases.There are no oscillations nor asymptotic regge actions at the order considered, nonetheless the amplitudes still induce non-trivial correlations between the two dipoles.We compute them within a mini-superspace description, finding positive correlations, decreasing in value with the immirzi parameter.We discuss some of the difficulties of non-simplicial foams, and provide a specific criterion to partially limit the proliferation of diagrams.