The automated calculation of Feynman diagrams in affine Toda field theory

Abstract

The purpose of this thesis is to calculate the residues of the poles of S matrix elements in the d(_6), e(_6), e(_7) and e(_8) Affine Toda Field theories. We will use the standard method of Feynman graphs in perturbation theory to calculate these results. Since there can be very many graphs, we will automate both the generation of these graphs and their subsequent calculation by the use of computer programs. This is the first ever machine calculation of residues in Toda Field theory. Affine Toda Field Theory has been studied in great depth for its integrability properties, and comparison will be made between the results we have generated, and the so called "exact" S matrices obtained by bootstrap and other properties. The results for the second and third order poles at positions predicted by the exact S matrix are tabulated for all of the algebras studied. In addition, for e(_6) all of the second and third order poles are tabulated regardless of the exact S matrix. The Feynman diagrams for the fourth order poles in d(_6) are generated, and the problem of calculating them is discussed.