  In this thesis special emphasis is put on the quantization of the spherically
reduced Einstein-massless-Klein-Gordon model using a first order approach for
geometric quantities, because phenomenologically it is probably the most
relevant of all dilaton models with matter. After a Hamiltonian BRST analysis
path integral quantization is performed using temporal gauge for the Cartan
variables. Retrospectively, the simpler Faddeev-Popov approach turns out to be
sufficient. It is possible to eliminate all unphysical and geometric quantities
establishing a non-local and non-polynomial action depending solely on the
scalar field and on some integration constants, fixed by suitable boundary
conditions on the asymptotic effective line element.
  Then, attention is turned to the evaluation of the (two) lowest order tree
vertices, explicitly assuming a perturbative expansion in the scalar field
being valid. Each of them diverges, but unexpected cancellations yield a finite
S-matrix element when both contributions are summed. The phenomenon of a
"virtual black hole" -- already encountered in the simpler case of minimally
coupled scalars in two dimensions -- occurs, as the study of the (matter
dependent) metric reveals. A discussion of the scattering amplitude leads to
the prediction of gravitational decay of spherical waves, a novel physical
phenomenon. Several possible extensions conclude this dissertation.
