Boundary Exchange Algebras and Scattering on the Half Line

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