Quantization and spacetime topology

We consider classical and quantum dynamics of a free particle in de Sitterʹs spacetimes with different topologies to see what happens to spacetime singularities of removable type in quantum theory. We find an 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 spacetime enables quantization of particle dynamics in all considered cases.