Poisson bracket algebra for chiral group elements in the WZNW model

In this paper, the authors examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the Poisson bracket algebra for left- and right-moving chiral group elements. The authors' computations apply for arbitrary groups and arbitrary boundary conditions, the latter being characterized by the monodromy matrix. Unlike previous treatments, the Poisson brackets do not require specifying a particular parametrization of the group valued fields in terms of angles spanning the group. The authors do however find it necessary to make a gauge choice, as the chiral group elements are not gauge invariant observables. (On the other hand, the 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 the quantum theory