CONSERVATION-LAWS FOR THE CLASSICAL TODA FIELD-THEORIES

Some explicit calculations of the conservation laws for classical (aff ine) Toda field theories, and some generalizations of these models are performed. We show that there is a huge class of generalized models w hich have an infinite set of conservation laws, with their integrated charges being in involution. Amongst these models we find that only th e A(m) and A(m)(1) (m greater-than-or-equal-to 2) Toda field theories admit such conservation laws for spin-3. The explicit calculations of spin-4 and spin-5 conservation laws in the (affine) Toda models are pr esented. Our perhaps most interesting finding is that there exist cons ervation laws in the A(m) models (m greater-than-or-equal-to 4) which have a different origin than the exponents of the corresponding affine theory or the energy-momentum tensor of a conformal theory.