Causality in Spin Foam Models

TL;DR

This paper introduces the concept of causal spin foams by computing the causal propagator in loop quantum gravity, revealing a sum over causally structured two-surfaces and unifying causal evolution models within this framework.

Contribution

It defines the novel concept of causal spin foams and demonstrates their relation to existing causal evolution models in loop quantum gravity.

Findings

Causal propagator expressed as a sum over branched, colored two-surfaces.

Introduction of the causal spin foam structure.

Causal evolution models are encompassed by causal spin foams.

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.