Causal structure in spin-foams

TL;DR

This paper explores how causality is represented in spin-foam models for quantum gravity, proposing a causal version of the EPRL model and examining its role in semiclassical spacetime reconstruction.

Contribution

It introduces a causal formulation of the EPRL spin-foam model and clarifies the physical meaning of orientation as a dynamical variable.

Findings

Proposes a causal spin-foam model based on orientation as a dynamical variable.

Analyzes the role of causal structure in reconstructing semiclassical spacetime.

Provides insights into encoding causality in quantum gravity models.

Abstract

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin-foam models for quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin-foam model and discuss the role of the causal structure in the reconstruction of a semiclassical spacetime geometry.