2 research outputs found
Quantum particle on hyperboloid
We present quantization of particle dynamics on one-sheet hyperboloid
embedded in three dimensional Minkowski space. Taking account of all global
symmetries enables unique quantization. Making use of topology of canonical
variables not only simplifies calculations but also gives proper framework for
analysis.Comment: 7 pages, no figures, revtex
Quantization and spacetime topology
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.Comment: Class. Quantum Grav. 20 (2003) 2491-2507; no figures, RevTeX