A spin foam model for general Lorentzian 4-geometries

TL;DR

This paper develops a new spin foam model for Lorentzian 4-geometries by deriving simplicity constraints that unify spacelike and timelike surfaces, leading to a discrete area spectrum.

Contribution

It introduces a novel method for deriving simplicity constraints using coherent states, extending the EPRL model to general Lorentzian geometries.

Findings

Consistent constraints for spacelike geometries with EPRL model

New constraints for general Lorentzian geometries

Discrete area spectrum for surfaces of all types

Abstract

We derive simplicity constraints for the quantization of general Lorentzian 4-geometries. Our method is based on the correspondence between coherent states and classical bivectors and the minimization of associated uncertainties. For spacelike geometries, this scheme agrees with the master constraint method of the model by Engle, Pereira, Rovelli and Livine (EPRL). When it is applied to general Lorentzian geometries, we obtain new constraints that include the EPRL constraints as a special case. They imply a discrete area spectrum for both spacelike and timelike surfaces. We use these constraints to define a spin foam model for general Lorentzian 4-geometries.