  A new parameterisation of the solutions of Toda field theory is introduced.
In this parameterisation, the solutions of the field equations are real,
well-defined functions on space-time, 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 developed to study the Toda theory, we
extend these results to the non-Abelian Toda field theories.

High Energy Physics - Theory