Root Systems and Boundary Bootstrap

The principle of boundary bootstrap plays a significant role in the algebraic study of the purely elastic boundary reflection matrix Ka(θ) for integrable quantum field theory defined on a space-time with a boundary. However, general structure of that principle in the form as was originally introduced by Fring and Köberle has remained unclear. In terms of a new matrix Ja(θ) = √ Ka(θ)/Kā(iπ + θ), the boundary bootstrap takes a simple form. Incidentally, a hypothesised expression of the boundary reflection matrix for simply-laced ADE affine Toda field theory defined on a half line with the Neumann boundary condition is obtained in terms of geometrical quantities of root systems à la Dorey. [email protected] [email protected]