THE SPACE OF SOLUTIONS OF TODA FIELD-THEORY

A new parametrization of the solutions of Toda field theory is introdu ced. In this parameterization, the solutions of the field equations ar e real, well-defined functions on spacetime, which is taken to be two- dimensional Minkowski space or a cylinder. The global structure of the covariant phase space of Toda theory is examined and it is shown that it is isomorphic to the Hamiltonian phase space. The Poisson brackets of Toda theory are then calculated. Finally, using the methods develo ped to study the Toda theory, we extend these results to the non-Abeli an Toda field theories.