POISSON BRACKET ALGEBRA FOR CHIRAL GROUP ELEMENTS IN THE WZNW MODEL

We examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the PoiSson bracket algebra for left- and Fight-moving chiral group elements. Our computations apply for arbitrary groups and arbitrary boundary conditions, die latter being characterized by die monodromy matrix. Unlike in previous treatments, the Poisson brackets do not require specifying a particular parametrization of the group valued fields in terms of angles spanning die group. We do however find it necessary to make a gauge choice, as the chiral group elements are not gauge invariant observables. (On die other hand, die quadratic form of the Poisson brackets may be defined independently of a gauge fixing.) Gauge invariant observables can be formed from the monodromy matrix and these observbles are seen to commute in die quantum theory.