  Some algebraic aspects of field quantization in space-time with boundaries
are discussed. We introduce an associative algebra, whose exchange properties
are inferred from the scattering processes in integrable models with reflecting
boundary conditions on the half line. The basic properties of this algebra are
established and the Fock representations associated with certain involutions
are derived. We apply these results for the construction of quantum fields and
for the study of scattering on the half line.
