Models of Topology Change

TL;DR

This paper explores how boundary condition modifications enable continuous topology change in quantum systems, with implications for entanglement, experimental realization, and interpretations of quantum mechanics.

Contribution

It introduces a framework for topology change via boundary conditions, providing examples, entanglement analysis, and potential experimental approaches.

Findings

Continuous interpolation among topologically distinct quantum states

Calculation of entanglement entropy during topology change

Proposed experimental realization of boundary condition effects

Abstract

We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of entanglement entropy production. We discuss approximate realization of boundary conditions through appropriate interactions, thus suggesting a route to possible experimental realization. We give a theoretical application to quantization of singular Hamiltonians, and give tangible form to the "many worlds" interpretation of wave functions.