Spin foam models as energetic causal sets

TL;DR

This paper develops a spin foam model that functions as an energetic causal set, introducing a novel mechanism for space-time emergence through energy-momentum flow and torsion constraints, advancing quantum gravity research.

Contribution

It constructs a spin foam model as an energetic causal set, incorporating torsion constraints and new momentum definitions related to tetrahedral volumes, linking connection and metric dynamics.

Findings

Integrates energetic causal sets with spin foam models.

Introduces volume-based momenta at events, enabling space-time emergence.

Addresses torsion constraints missing in previous models.

Abstract

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. 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 arXiv:1407.0025, and this construction makes use of results used there. What makes a spin foam model also an energetic causal set is Wieland's identification of new 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.