Poisson Structure and Moyal Quantisation of the Liouville Theory

Details Poisson Structure and Moyal Quantisation of the Liouville Theory Poisson Structure and Moyal Quantisation of the Liouville Theory

2001-05-30

arxiv.org/abs/hep-th/0105306v1

Nucl.Phys. B619 (2001) 232-256

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, LaTeX, no figures

Scientific paper

10.1016/S0550-3213(01)00525-9

The symplectic and Poisson structures of the Liouville theory are derived from the symplectic form of 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 chiral 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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