A Spin-Statistics Theorem for Certain Topological Geons

TL;DR

This paper explores how topological geons in quantum gravity can exhibit nontrivial spin and statistics, and demonstrates that a spin-statistics correlation holds for certain geons in a topology-changing framework.

Contribution

It establishes a spin-statistics theorem for topological geons within a sum-over-histories quantum gravity approach involving topology change.

Findings

Non-chiral abelian geons satisfy spin-statistics correlation with topology change.

Wave functions described by functional integrals over metrics on specific four-manifolds.

Topology change enables anomalous spin-statistics pairings in quantum gravity.

Abstract

We review the mechanism in quantum gravity whereby topological geons, particles made from non-trivial spatial topology, are endowed with nontrivial spin and statistics. In a theory without topology change there is no obstruction to ``anomalous'' spin-statistics pairings for geons. However, in a sum-over-histories formulation including topology change, we show that non-chiral abelian geons do satisfy a spin-statistics correlation if they are described by a wave function which is given by a functional integral over metrics on a particular four-manifold. This manifold describes a topology changing process which creates a pair of geons from $R^3$.