Quantization and spacetime topology
arXiv:gr-qc/0210023 · doi:10.1088/0264-9381/20/13/303
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.
Class. Quantum Grav. 20 (2003) 2491-2507; no figures, RevTeX4