Poisson bracket algebra for chiral group elements in the WZNW model

Journal Article · Wed Sep 30 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92002799· OSTI ID:7158929

Bimonte, G ^[1]; Salomomson, P ^[2]; Simoni, A; Stern, A ^[3]

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1. Syracuse Univ., NY (United States). Dept. of Physics
2. Inst. of Theoretical Physics, S-41296, Goteborg (Sweden)
3. Dipt. di Scienze Fisiche dell' Univ. di Napoli, Mostra d'Oltremare pad. 19, 80125 Napoli (Italy)

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.

• OSTI ID: 7158929
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:24; ISSN IMPAEF; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
BOUNDARY CONDITIONS
CHIRAL SYMMETRY
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
MATHEMATICS
MATRIX ELEMENTS
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
QUANTUM FIELD THEORY
SYMMETRY