CROSSING AND ANTISOLITONS IN AFFINE TODA THEORIES

Affine Toda theory is a relativistic integrable theory in two dimensio ns possessing solutions describing a number of different species of so litons when the coupling is chosen to be imaginary. These nevertheless carry real energy and momentum. To each species of soliton there has to correspond an antisoliton species. There are two different ways of realising the antisoliton whose equivalence is shown to follow from a surprising identity satisfied within the underlying affine Kac-Moody g roup. This is the classical analogue of the crossing property of analy tic S-matrix theory. Since a complex parameter related to the coordina te of the soliton is inverted, this identity implies a sort of modular transformation property of the soliton solution. The results simplify calculations of explicit soliton solutions.