Causality in spin foam models

Abstract

We compute Teitelboim's causal propagator in the context of canonical loop quantum gravity. For the Lorentzian signature, we find that the resultant power series can be expressed as a sum over branched, colored two-surfaces with an intrinsic causal structure. This leads us to define a general structure which we call a ``causal spin foam.'' We also demonstrate that the causal evolution models for spin networks fall in the general class of causal spin foams.