Reduction of the affine Toda field theory

The equations of motion of affine Toda field theory is a coupled equation for r fields, where r is the rank of the underlying Lie algebra. In some cases, it admits a reduction, in which the equation is satisfied by fewer than r fields. We investigate various 'dimension-one' reductions, in which only one field remains. These correspond to the classical images of 'solitons' and are expected to play an important role in the imaginary- coupling regime of affine Toda field theory which is closely related to integrable deformation of conformal field theory. Quantum field-theoretical data such as masses (especially those with integer (mass)2) and the three-point couplings are shown to be important for the 'dimension-one' reduction. (orig.)