Spin foam models as energetic causal sets

Energetic causal sets are causal sets endowed by a flow of energy-momentum between causally related events. These incorporate a novel mechanism for the emergence of space-time from causal relations [M. Cortes and L. Smolin, Phys. Rev. D 90, 084007 (2014); Phys. Rev. D 90, 044035 (2014)]. Here we construct a spin foam model which is also an energetic causal set model. This model is closely related to the model introduced in parallel by Wolfgang Wieland in [Classical Quantum Gravity 32, 015016 (2015)]. What makes a spin foam model also an energetic causal set is Wieland's identification of new degrees of freedom analogous to momenta, conserved at events (or four-simplices), whose norms are not mass, but the volume of tetrahedra. This realizes the torsion constraints, which are missing in previous spin foam models, and are needed to relate the connection dynamics to those of the metric, as in general relativity. This identification makes it possible to apply the new mechanism for the emergence of space-time to a spin foam model. Our formulation also makes use of Markopoulou's causal formulation of spin foams [arXiv:gr-qc/9704013]. These are generated by evolving spin networks with dual Pachner moves. This endows the spin foam history with causal structure given by a partial ordering of the events which are dual to four-simplices.