Alternative Canonical Formalism for the Wess-Zumino-Witten Model

We study a canonical quantization of the Wess{Zumino{Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to in nity keeping the di erence xed. The quantum theory is equivalent to a generalized Thirring model, with left and right handed fermions transforming under di erent representations of the symmetry group. We also point out that the classical WZW model with a compact target space has a canonical formalism in which the current algebra is an a ne Lie algebra of non{compact type. Also, there are some non{unitary quantizations of the WZW model in which there is invariance only under half the conformal algebra (one copy of the Virasoro algebra). UR-1336 hep-th/9312178 December 1993