Generalized Toda field theories Original Research Article

In this paper we introduce a unified approach to Toda field theories which allows us to formulate the classes of An, Bn and Cn models as unique models involving an arbitrary continuous parameter v. For certain values of v, the model describes the standard Toda theories. For other values of v 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.