Aharonov-Bohm effect on the Poincare disk

We consider formal quantum Hamiltonian of a charged particle on the Poincare disk in the presence of an Aharonov-Bohm magnetic vortex and a uniform magnetic field. It is shown that this Hamiltonian admits a four-parameter family of self-adjoint extensions. Its resolvent and the density of states are calculated for natural values of the extension parameters. (c) 2007 American Institute of Physics.