  We consider dynamics of massless particle in 2d spacetimes with constant
curvature. We analyze different examples of spacetime. Dynamical integrals are
constructed from spacetime symmetry related to $sl(2.{\bf R})$ algebra.
Mass-shell condition restricts dynamical integrals to a cone (without vertex)
which defines physical-phase space. We parametrize the cone by canonical
coordinates. Canonical quantization with definite choice of operator ordering
leads to unitary irreducible representations of $SO_\uparrow (2.1)$ group.
