Title:

Integrable quantum field theories, in the bulk and with a boundary

In this thesis, we consider the massive field theories in 1+1 dimensions known as affine Toda quantum field theories. These have the special property that they possess an infinite number of conserved quantities, a feature which greatly simplifies their study, and makes extracting exact information about them a tractable problem. We consider these theories both in the full space (the bulk) and in the half space bounded by an impenetrable boundary at x = 0. In particular, we consider their fundamental objects: the scattering matrices in the bulk, and the reflection factors at the boundary, both of which can be found in a closed form. In Chapter 1, we provide a general introduction to the topic before going on, in Chapter 2, to consider the simplest ATFT—the sineGordon model—with a boundary. We begin by studying the classical limit, finding quite a clear picture of the boundary structure we can expect in the quantum case, which is introduced in Chapter 3. We obtain the boundstate structure for all integrable boundary conditions, as well as the corresponding reflection factors. This structure turns out to be much richer than had hitherto been imagined. We then consider more general ATFTs in the bulk. The sineGordon model is based on a(^(1))(_1), but there is an ATFT for any semisimple Lie algebra. This underlying structure is known to show up in their Smatrices, but the path back to the parameters in the Lagrangian is still unclear. We investigate this, our main result being the discovery of a "generalised bootstrap" equation which explicitly encodes the Lie algebra into the Smatrix. This leads to a number of new Smatrix identities, as well as a generalisation of the idea that the conserved charges of the theory form an eigenvector of the Cartan matrix. Finally our results are summarised in Chapter 5, and possible directions for further study are highlighted.
