Geon Statistics and UIR's of the Mapping Class Group

TL;DR

This paper explores how topological geons in quantum gravity influence particle properties, revealing new statistical behaviors and symmetries linked to the topology of space.

Contribution

It introduces a novel interpretation of topological parameters as geon properties and uncovers new particle identities and statistics arising from these topological effects.

Findings

Geons exhibit new patterns of particle identity.

Geon statistics can be described by subgroup representations.

Topological parameters relate to geon properties.

Abstract

Quantum Gravity admits topological excitations of microscopic scale which can manifest themselves as particles --- topological geons. Non-trivial spatial topology also brings into the theory free parameters analogous to the $\theta$-angle of QCD. We show that these parameters can be interpreted in terms of geon properties. We also find that, for certain values of the parameters, the geons exhibit new patterns of particle identity together with new types of statistics. Geon indistinguishability in such a case is expressed by a proper subgroup of the permutation group and geon statistics by a (possibly projective) representation of the subgroup.