Quantization and spacetime topology

TL;DR

This paper investigates how the global topology of de Sitter space-times influences the classical and quantum behavior of free particles, revealing that global properties allow for consistent quantization across different topologies.

Contribution

It provides a detailed analysis of classical and quantum dynamics of particles in various topologically distinct de Sitter space-times, highlighting the role of global properties in quantization.

Findings

Quantum dynamics is well-defined when global properties are considered.

Classical solutions are explicitly obtained for different topologies.

Quantization is possible for all considered topologies due to global considerations.

Abstract

We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the classical dynamics. The quantum dynamics is solved by finding an essentially self-adjoint representation of the algebra of observables integrable to the unitary representations of the symmetry group of each considered gravitational system. The dynamics of a massless particle is obtained in the zero-mass limit of the massive case. Our results indicate that taking account of global properties of space-time enables quantization of particle dynamics in all considered cases.