Path integral treatment for a Coulomb system constrained on D-dimensional sphere and hyperboloid

The propagator relating to the evolution of a particle on the D-sphere and the D-pseudosphere, subjected to the Coulomb potential, was reconsidered in the Faddeev–Senjanovic formalism. The mid-point is privileged. The space–time transformations used make it possible to regularize the singularity and to bring back the problem to its dynamical symmetry SU (1, 1).