SOLITONS AND VERTEX OPERATORS IN TWISTED AFFINE TODA FIELD-THEORIES

Affine Toda field theories in two dimensions constitute families of in tegrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantu m excitations of the fields display interesting patterns in their mass es and coupling which have recently been shown to extend to the classi cal soliton solutions arising when the couplings are imaginary. Here t hese results are extended from the untwisted to the twisted algebras. The new soliton solutions and their masses are found by a folding proc edure which can be applied to the affine Kac-Moody algebras themselves to provide new insights into their structures. The relevant foldings are related to inner automorphisms of the associated finite dimensiona l Lie group which are calculated explicitly and related to what is kno wn as the twisted Coxeter element. The fact that the twisted affine Ka c-Moody algebras possess vertex operator constructions emerges natural ly and is relevant to the soliton solutions.