Topology of spacetime and quantization of particle dynamics

TL;DR

This paper investigates how the global topology of de Sitter spacetime influences the quantization of particle dynamics, emphasizing the importance of classical system properties in quantum representations.

Contribution

It demonstrates that the quantization outcome is highly dependent on the spacetime's global topology and provides self-adjoint representations of the observable algebra for different topologies.

Findings

Quantization varies with spacetime topology

Self-adjoint representations are constructed for each case

Global properties determine symmetry preservation

Abstract

We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially self-adjoint representations of the algebra of observables for each system. Quantization based on global properties of a classical system accounts properly its symmetries.