PURE WESS-ZUMINO ACTIONS IN 1+1 DIMENSIONAL NONLINEAR σ-MODELS

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We examine the Hamiltonian formulation for a 1+1 dimensional nonlinear σ-model where the action is given solely by a Wess-Zumino term. The theory corresponds to the Wess-Zumino-Witten model where the standard nonlinear chiral model action is absent. We find that the Poisson bracket algebra for the currents corresponds to a Kac-Moody algebra. The system, however, contains second class constraints which we eliminate via the construction of Dirac brackets. The Kac-Moody algebra is then not realized by the Dirac brackets. Instead, new (nonlocal) terms appear in the algebra of the conserved currents which appear to obstruct quantization.