On extended structures in affine Toda field theory

Abstract

Two areas of affine Toda field theory are explored in this thesis. First the introduction of a boundary into the real coupling affine Toda field theory. It has been shown by other authors that affine Toda field theory stays an integrable theory for certain boundaries. One such theory is the one corresponding to Its integrable boundary condition is described by two continuous parameters. Also, it is continuously connected to the natural Neumann condition, i.e. vanishing space derivative of the fields at the boundary. Classical reflection factors of incoming plane waves in the background of a static soliton solution are calculated for this theory. They fulfil a classical reflection bootstrap equation which is the classical limit of the reflection bootstrap equation for reflection matrices. The second part is concerned with the the αη(^1) affine Toda field theory with imaginary coupling. The behaviour of oscillatory solitonic solutions, breathers is investigated. Explicit construction for breather solution are given. They originate from two soliton solutions. It is found that there are two different types of breathers depending on their constituent solitons. The constituent solitons are either of the same species or are anti-species of each other. Also, the topological charges of breather solutions are calculated and they are either zero or equal to a certain one soliton solution. These topological charges lie in the tensor product representation of the fundamental representations associated with the topological charges of the constituent solitons. The breather masses are, as expected, less than the sum of the masses of the constituent solitons.