Quantum mechanics in multiply connected spaces

TL;DR

This paper explores how the topology of multiply connected spaces influences quantum observables, revealing that compactified spaces can induce intrinsic spin-like properties in particles.

Contribution

It demonstrates that the topology of configuration space can determine quantum properties like angular momentum and spin, especially in compactified Kaluza-Klein spaces.

Findings

Multiply connected spaces affect quantum observables.

Compactified Kaluza-Klein spaces induce half-integer angular momentum.

Intrinsic spin can arise from space topology.

Abstract

This paper analyses quantum mechanics in multiply connected spaces. It is shown that the multiple connectedness of the configuration space of a physical system can determine the quantum nature of physical observables, such as the angular momentum. In particular, quantum mechanics in compactified Kaluza-Klein spaces is examined. These compactified spaces give rise to an additional angular momentum which can adopt half-integer values and, therefore, may be identified with the intrinsic spin of a quantum particle.