  We present a general formalism describing a propagation of an arbitrary
multiparticle wave packet in a one-dimensional multimode chiral channel coupled
to an ensemble of emitters which are distributed at arbitrary positions. The
formalism is based on a direct and exact resummation of diagrammatic series for
the multiparticle scattering matrix. It is complimentary to the Bethe Ansatz
and to approaches based on equations of motion, and it reveals a simple and
transparent structure of scattering states. In particular, we demonstrate how
this formalism works on various examples, including scattering of one- and
two-photon states off two- and three-level emitters, off an array of emitters
as well as scattering of coherent light. We argue that this formalism can be
constructively used for study of scattering of an arbitrary initial photonic
state off emitters with arbitrary degree of complexity.
