The Spin-Statistics Connection in Quantum Gravity

TL;DR

This paper explores the spin-statistics connection in quantum gravity, revealing a modified relation for topological geons using an algebraic formalism and superselection assumptions, challenging traditional theorems.

Contribution

It introduces an algebraic framework for topological geons in quantum gravity, demonstrating a new spin-statistics relation under superselection assumptions.

Findings

Traditional spin-statistics theorem is violated for geons.

A new spin-statistics relation emerges with superselected fluxes.

The approach aligns with conventional quantum gravity formulations.

Abstract

It is well-known that is spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of "observables" is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian "charge" and "magnetic flux". We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also show how our approach fits into conventional formulations of quantum gravity.