3 research outputs found
Coherent state quantization of a particle in de Sitter space
We present a coherent state quantization of the dynamics of a relativistic
test particle on a one-sheet hyperboloid embedded in a three-dimensional
Minkowski space. The group SO_0(1,2) is considered to be the symmetry group of
the system. Our procedure relies on the choice of coherent states of the motion
on a circle. The coherent state realization of the principal series
representation of SO_0(1,2) seems to be a new result.Comment: Journal of Physics A: Mathematical and General, vol. 37, in pres
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