Abstract
The symplectic and Poisson structures of the Liouville theory are derived from the SL(2, R) WZNW theory by gauge invariant Hamiltonian reduction. Causal non-equal time Poisson brackets for a Liouville field are presented. Using the symmetries of the Liouville theory, symbols of local fields are constructed and their ∗-products calculated. Quantum deformations consistent with the canonical quantisation result, and a non-equal time commutator is given.
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