Fermion spins in loop quantum gravity

TL;DR

This paper explores how fermion spin observables behave within loop quantum gravity, revealing that entanglement with gravity influences spin properties and could have observable effects on quantum geometry.

Contribution

It introduces gauge-invariant fermion spin observables in loop quantum gravity and analyzes their properties, highlighting new effects due to gravity-fermion entanglement.

Findings

Spin spectra resemble quantum mechanics counterparts

Entanglement affects spin alignment and geometry

Potential observable effects on quantum geometry

Abstract

We define and study kinematical observables involving fermion spin, such as the total spin of a collection of particles, in loop quantum gravity. Due to the requirement of gauge invariance, the relevant quantum states contain strong entanglement between gravity and fermionic degrees of freedom. Interestingly we find that properties and spectra of the observables are nevertheless similar to their counterparts from quantum mechanics. However, there are also new effects. Due to the entanglement between gravity and fermionic degrees of freedom, alignment of quantum spins has consequences for quantized geometry. We sketch a particular effect of this kind that may in principle be observable.