Poisson Structure and Moyal Quantisation of the Liouville Theory

Abstract

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.

32 pages, LaTeX, no figures

References in corpus (2)

• Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids
• A Proposal for a Differential Calculus in Quantum Mechanics

Cited by in corpus (6)

• Correlation Functions and Vertex Operators of Liouville Theory
• On the S-matrix of Liouville theory
• A Causal Algebra for Liouville Exponentials
• 4d Chern-Simons Theory as a 3d Toda Theory, and a 3d-2d Correspondence
• Quantisation of Gauged SL(2,R) WZNW Theories
• Causal Poisson bracket via deformation quantization