BOUNDARY EXCHANGE ALGEBRAS AND SCATTERING ON THE HALF LINE

Some algebraic aspects of field quantization in space-time with bounda ries are discussed. We introduce an associative algebra B-R, whose exc hange properties are inferred from the scattering processes in integra ble models with reflecting boundary conditions on the half line. The b asic properties of B-R are established and the Fock representations as sociated with certain involutions in B-R are derived. We apply these r esults for the construction of quantum fields and for the study of sca ttering on the half line.