  We develop quantization aspects of our Liouville approach to non-critical
strings, proposing a path-integral formulation of a second quantization of
string theory, that incorporates naturally the couplings of string sources to
background fields. Such couplings are characteristic of macroscopic string
solutions and/or $D$-brane theories. Resummation over world-sheet genera in the
presence of stringy ($\sigma$-model) soliton backgrounds, and recoil effects
associated with logarithmic operators on the world sheet, play a crucial r\^ole
in inducing such sources as well-defined renormalization-group counterterms.
Using our Liouville renormalization group approach, we derive the appropriate
second-order equation of motion for the $D$ brane. We discuss within this
approach the appearance of open strings, whose ends carry non-trivial
Chan-Paton-like quantum numbers related to the $W_\infty$ charges of
two-dimensional string black holes.
