Quantum geometric maps and their properties

TL;DR

This paper provides a general framework for quantum geometric maps in spin foam models of quantum gravity, analyzing their properties and the impact of simplicity constraints across different models.

Contribution

It offers a unified definition of quantum geometric maps applicable to all current spin foam models and examines how simplicity constraints influence their features.

Findings

Unified framework for quantum geometric maps

Analysis of simplicity constraints effects

Comparison across multiple spin foam models

Abstract

Quantum geometric maps, which relate SU(2) spin networks and Lorentz covariant projected spin networks, are an important ingredient of spin foam models (and tensorial group field theories) for 4-dimensional quantum gravity. We give a general definition of such maps, that encompasses all current spin foam models, and we investigate their properties at such a general level. We then specialize the definition to see how the precise implementation of simplicity constraints affects features of the quantum geometric maps in specific models.