Starting with a two-cocycle globally defined on a Lie group G, the Lagrangian system on G is constructed whose Lagrangian is quasi-invariant under a right translation canonically lifted to the tangent bundle TG. A direct consequence of the quasi-invariance is the appearance of central extensions in the Noether-symmetry algebra. Then, it is shown that the kinematical sector of such a model realizes, through a symplectic reduction, the Kirillov–Kostant symplectic structure on the coadjoint orbit of the Lie group with the central extensions. The generalization to a ‘‘higher-dimensional’’ theory of the Wess–Zumino–Witten-type is also discussed herein.
The algebraic structure of the chirally gauged Wess-Zumino-Witten model is studied from the Hamiltonian point of view. The consistent chiral anomaly, which is reproduced at the tree level in this model, is related to the Schwinger term of the Gauss-law algebra through descent equations constructed with phase-space differential forms. The descent equations express the effects of the consistent anomaly upon the symplectic structure of the theory, and provide the Hamiltonian analogue of the Wess-Zumino consistency condition in the Weyl gauge. We also clarify the canonical structure of the ungauged Wess-Zumino-Witten model, and the algebra associated with the global Noether symmetry is derived.PACS number(s): 1 l. lO.Ef, 02.40. +m, 11.30.Rd
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