Generalized Toda field theories

In this paper we introduce a unified approach to Toda field theories which 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 certain values of nu, the model describes the standard Toda theories. For other values of nu it defines a class of models that involve infinitely many fields. These models interpolate between the various standard Toda field theories. They are conformally invariant and possess infinitely many conserved higher-spin currents thus making them candidates for a new set of integrable systems. A general construction is performed, which can effectively be used for the derivation of explicit forms of particular higher-spin currents. We also study the currents in a different representation in which they are linear in the dynamical variables having, however, a non-linear Poisson bracket algebra. An explicit formula for this Poisson structure is found.