  The propagator of the spinless Aharonov-Bohm-Coulomb system is derived by
following the Duru-Kleinert method. We use this propagator to explore the
spin-1/2 Aharonov-Bohm-Coulomb system which contains a point interaction as a
Zeeman term. Incorporation of the self-adjoint extension method into the
Green's function formalism properly allows us to derive the finite propagator
of the spin-1/2 Aharonov-Bohm-Coulomb system. As a by-product, the relation
between the self-adjoint extension parameter and the bare coupling constant is
obtained. Bound-state energy spectra of both spinless and spin-1/2
Aharonov-Bohm-Coulomb systems are examined.
