Observables in 3d spinfoam quantum gravity with fermions

TL;DR

This paper investigates expectation values of observables in 3D spinfoam quantum gravity coupled with massless Dirac fermions, extending previous models and analyzing gauge symmetries and fermionic observables.

Contribution

It introduces a new extension of the 3D spinfoam model to include massless fermions, and develops methods to compute fermionic and gravity observables within this framework.

Findings

Derived vertex amplitudes for gauge-invariant observables

Expressed fermionic propagators as evaluations of spin networks

Performed Berezin integration over fermionic fields

Abstract

We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce observables, analyse their symmetries and the corresponding proper gauge fixing. The Berezin integral over the fermionic fields is performed and the fermionic observables are expanded in open paths and closed loops associated to pure quantum gravity observables. We obtain the vertex amplitudes for gauge-invariant observables, while the expectation values of gauge-variant observables, such as the fermion propagator, are given by the evaluation of particular spin networks.