Boundary bootstrap principle in two-dimensional integrable quantum field theories

We study the reflection amplitudes of affine Toda field theories with boundary, following the ideas developed by Fring and Koberle and focusing our attention on the $E_n$ series elements, because of their interesting structure of higher order poles. We also investigate the corresponding minimal reflection matrices, finding, with respect to the bulk case, a more complicated relation between the spectra of bound states associated to the minimal and to the ‘‘dressed’’ amplitudes.