Causal spin foams

TL;DR

This paper explores how to incorporate causality into spin-foam models by distinguishing propagation directions, transforming triangulations into causal sets, and ensuring the models asymptotically reproduce the exponential of the Regge action, not a cosine.

Contribution

It introduces a method to impose causality on spin-foam models, clarifies the equivalence of existing prescriptions, and emphasizes the importance of the closure condition for space-like tetrahedra.

Findings

Causality can be imposed by separating forward and backward propagation.

The models asymptotically yield the exponential of the Regge action.

Different prescriptions for causality are shown to be equivalent.

Abstract

I discuss how to impose causality on spin-foam models, separating forward and backward propagation, turning a given triangulation to a 'causal set', and giving asymptotically the exponential of the Regge action, not a cosine. I show the equivalence of the prescriptions which have been proposed to achieve this. Essential to the argument is the closure condition for the 4-simplices, all made of space-like tetrahedra.