A path integral formalism is developed to study the interaction of an arbit
rary curved Dirichlet (D-) string with elementary excitations of the fundum
ental (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 m
oving along a curved trajectory. Using this vertex, an attempt is further m
ade to quantize the D-string coordinates and to compute the quantum amplitu
de for scattering between elementary excitations of the D- and F-strings. B
y studying the dependence on the Liouville mode for the D-string, it is fou
nd that the vertex in our approximation consists of an infinite tower of lo
cal vertex operators which are conformally invariant on their respective ma
ss-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 nontrivia
l when the dual extended objects are simultaneously present. Possible futur
e directions are suggested.