Boundary exchange algebras and scattering on the half line

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