Quantum Topology Change in (2 + 1)d

TL;DR

This paper explores the formal description of topological geons in (2+1)d spacetimes, enabling analysis of quantum topology change processes like geon creation and annihilation, with derived selection rules.

Contribution

It introduces a formalism separating topological degrees of freedom from metric degrees, facilitating the study of quantum topology change in (2+1)d spacetimes.

Findings

Formalism for topological geons and their degrees of freedom

Derived selection rules for quantum topology change

Framework for geon creation and annihilation processes

Abstract

The topology of orientable (2 + 1)d spacetimes can be captured by certain lumps of non-trivial topology called topological geons. They are the topological analogues of conventional solitons. We give a description of topological geons where the degrees of freedom related to topology are separated from the complete theory that contains metric (dynamical) degrees of freedom. The formalism also allows us to investigate processes of quantum topology change. They correspond to creation and annihilation of quantum geons. Selection rules for such processes are derived.