  A path integral formalism is developed to study the interaction of an
arbitrary curved Dirichlet (D-) string with elementary excitations of the
fundumental (F-) string in bosonic string theory. Up to the next to leading
order in the derivative expansion, we construct the properly renormalized
vertex operator, which generalizes the one previously obtained for a D-particle
moving along a curved trajectory. Using this vertex, an attempt is further made
to quantize the D-string coordinates and to compute the quantum amplitude for
scattering between elementary excitations of the D- and F-strings. By studying
the dependence on the Liouville mode for the D-string, it is found that the
vertex in our approximation consists of an infinite tower of local vertex
operators which are conformally invariant on their respective mass-shell. This
analysis indicates that, unlike the D-particle case, an off-shell extension of
the interaction vertex would be necessary to compute the full amplitude and
that the realization of symmetry can be quite non-trivial when the dual
extended objects are simultaneously present. Possible future directions are
suggested.
