Bosonic and fermionic statistics in nonperturbative quantum gravity

TL;DR

This paper investigates how the principle of general covariance in nonperturbative quantum gravity, specifically loop quantum gravity, allows for gravitational states with bosonic, fermionic, and mixed statistics, challenging traditional assumptions.

Contribution

It demonstrates that in loop quantum gravity, the space of gravitational states includes fermionic and mixed statistics, extending the understanding of quantum gravity beyond bosonic states.

Findings

Gravitational states can exhibit fermionic statistics.

The state space includes mixed statistics subspaces.

General covariance permits non-bosonic quantum states.

Abstract

The relation between spin and statistics in quantum field theory relies on Poincar\'e invariance, a symmetry that is lost in the presence of a gravitational field, and replaced in general relativity by the principle of general covariance. In a nonperturbative approach to quantum gravity, beyond the picture of gravitational perturbations propagating on a flat background, it is an open question whether the gravitational field must still satisfy a bosonic statistics. By implementing the principle of general covariance through the requirement of invariance under active diffeomorphisms in loop quantum gravity, we find that the space of kinematical states of the gravitational field includes not only bosonic states, but also subspaces of fermionic and mixed statistics.