GENERALIZED TODA FIELD-THEORIES

In this paper we introduce a unified approach to Toda field theories w hich allows us to formulate the classes of A(n), B-n and C-n models as unique models involving an arbitrary continuous parameter nu. For cer tain values of nu, the model describes the standard Toda theories. For other values of nu it defines a class of models that involve infinite ly many fields. These models interpolate between the various standard Toda field theories. They are conformally invariant and possess infini tely many conserved higher-spin currents thus making them candidates f or a new set of integrable systems. A general construction is performe d, which can effectively be used for the derivation of explicit forms of particular higher-spin currents. We also study the currents in a di fferent representation in which they are linear in the dynamical varia bles having, however, a non-linear Poisson bracket algebra. An explici t formula for this Poisson structure is found.