Quantum corrections to the classical reflection factor of the sinh-Gordon model

Abstract

This thesis studies the quantum reflection factor of the sinh-Gordon model under boundary conditions consistent with integrability. First, we review the affine Toda field theory in Chapter One. In particular, the classical and quantum integrability of the theory are reviewed on the whole line and on the half-line as well, that is, in the presence of a boundary. We next consider the sinh-Gordon model which is restricted to a half-line by boundary conditions maintaining integrability in Chapter Two. A perturbative calculation of the reflection factor is given to one loop order in the bulk coupling and to first order in the difference of the two parameters introduced at the boundary. The result provides a further verification of Ghoshal's formula. The calculation is consistent with a conjecture for the general dependence of the reflection factor on the boundary parameters and the bulk coupling. In Chapter Three, quantum corrections to the classical reflection factor of the sinh-Gordon model are studied up to second order in the difference of boundary data and to one loop order in the bulk coupling. Chapter Four deals with the quantum reflection factor for the sinh-Gordon model with general boundary conditions. The model is studied under boundary conditions which are compatible with integrability and in the framework of the conventional perturbation theory generalised to the affine Toda field theory. It is found that the general form of a subset of the related quantum corrections are hypergeometric functions. Finally, we sum up this thesis in Chapter Five along with some conclusions and suggestions for further future studies.