The Global Phase Space Structure of the Wess-Zumino-Witten Model

We present a new parametrisation of the space of solutions of the Wess-Zumino-Witten model on a cylinder, with target space a compact, connected Lie group G. Using the covariant canonical approach the phase space of the theory is shown to be the co-tangent bundle of the loop group of the Lie group G, in agreement with the result from the Hamiltonian approach. The Poisson brackets in this phase space are derived. Other formulations in the literature are shown to be obtained by locally-valid gauge-fixings in this phase space.