Affine Toda field theories on a half-line
This thesis is primarily concerned with the reflection factors of affine Toda field theories on the half-line x ≤ 0. First, we consider the classical background configurations of low rank a,(^(1)) affine Toda theories with a boundary, constructed by the analytic-continuation of soliton solutions of the corresponding imaginary-coupling theories. We show that only a small subset of such solutions provide acceptable vacuum configurations. These are classified according to the integrable boundary conditions they obey and their classical reflection factors are considered. We next consider the quantum theories, where we aim to provide evidence for or against exact reflection factors proposed in the literature. We do this by explicit calculation of the low-order coupling dependence of the reflection factors via perturbation theory. Two particular examples are considered in detail. The first is the O(β(^2)) calculation for a(_2)(^1) affine Toda field theory with the boundary condition. This will be a good example to study since it is the subject of many conjectured exact reflection factors and also demonstrates the renormalisation of the boundary potential required to retain quantum integrability. The second example will be the O(β(^4)) calculation for sinh-Gordon theory. In light of the added complexity of the higher-order calculation we consider only the Neumann boundary condition. Finally we look at the renormalisation of sinh-Gordon theory and its duality properties.