Aspects of affine Toda field theory

Affine Toda field theory is a theory of r scalar fields in two-dimensional Minkowski space-time, where r is the rank of a compact semi-simple Lie algebra g. A reasonable question to ask is whether the classical integrability survives into the quantum field theory and, if so, what is the spectrum and to what extent is it possible to calculate explicitly quantities of interest such as S-matrices and form factors. Recent discoveries leave no doubt that these relatively simple two-dimensional models have much structure and their study will be informative. In this short review, the ADE series of Lie algebras is singled out for special attention. 27 refs