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 infinity keeping the difference fixed. The quantum theory is equivalent to a generalized Thirring model, with left- and right-handed fermions transforming under different representations of the symmetry group. We also note that the classical WZW model with a compact target space has a canonical formalism in which the current algebra is an affine Lie algebra of the noncompact type. In addition, there are some nonunitary quantizations of WZW model in which there is invariance only under half the conformal algebra (one copy of the Virasoro algebra).