  We study interactions of string coherent states in the DDF (after Di Vecchia,
Del Giudice, Fubini) formalism. For simplicity we focus on open bosonic
strings. After reviewing basic properties of DDF operators and of excited open
strings, we present some classical profiles and show how they become more and
more compact as the number of harmonics increases at fixed mass. We then
compute various three- and four-point amplitudes with insertions of coherent
states, tachyons and vector bosons on the boundary of the disk relying on a
convenient choice of reference null momenta. We find that the amplitudes
exponentiate in a rather subtle and interesting way. We then study the
high-energy fixed-angle limit, dominated by a saddle-point when coherent states
are present, and the soft behaviour as the momentum of a vector boson is taken
to zero. We briefly comment on generalisation of our analysis to multiple
intersecting and magnetised D-branes and to closed strings.
