Fermions in three-dimensional spinfoam quantum gravity

TL;DR

This paper develops a spinfoam model for three-dimensional quantum gravity coupled with massive fermions, incorporating quantum torsion effects and modifications to curvature, advancing the understanding of matter-gravity interactions in quantum regimes.

Contribution

It introduces a novel spinfoam framework for fermions in 3D quantum gravity, including quantum torsion effects and curvature modifications, using a finite inverse mass expansion.

Findings

Derived a path integral as a sum over fermionic loops

Modified intertwining operators to include quantum torsion effects

Modeled non-trivial curvature through vertex amplitude modifications

Abstract

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity coupled to spinors. The technique used is based on a finite expansion in inverse fermion masses leading to the computation of the vacuum to vacuum transition amplitude of the theory. The path integral is derived as a sum over closed fermionic loops wrapping around the spinfoam. The effects of quantum torsion are realised as a modification of the intertwining operators assigned to the edges of the two-complex, in accordance with loop quantum gravity. The creation of non-trivial curvature is modelled by a modification of the pure gravity vertex amplitudes. The appendix contains a review of the geometrical and algebraic structures underlying the classical coupling of fermions to three dimensional gravity.