Geometry of 2d spacetime and quantization of particle dynamics

We analyze classical and quantum dynamics of a relativistic particle in 2d spacetimes with constant curvature. We show that global symmetries of spacetime specify the symmetries of physical phase-space and the corresponding quantum theory. To quantize the systems we parametrize the physical phase-space by canonical coordinates, Canonical quantization leads to unitary irreducible representations of SO (up arrow) (2.1) group. (C) 1999 Published by Elsevier Science B.V. All rights reserved.