POISSON BRACKET ALGEBRA FOR CHIRAL GROUP ELEMENTS IN THE WZNW MODEL

DOI10.1142/S0217751X92002799zbMATH Open0972.81629arXivhep-th/9201062OpenAlexW3102261821MaRDI QIDQ4523782

No author found.

Publication date: 14 January 2001

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Abstract: We 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. Our computations apply for arbitrary groups and boundary conditions, the latter being characterized by the monodromy matrix. Unlike in previous treatments, they do not require specifying a particular parametrization of the group valued fields in terms of angles spanning the group. We 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 independent of a gauge fixing.) Gauge invariant observables can be formed from the monodromy matrix and these observables are seen to commute in the quantum theory.

Full work available at URL: https://arxiv.org/abs/hep-th/9201062

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Applications of Lie (super)algebras to physics, etc. (17B81) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)