http://cds.cern.ch/record/385927/files/9904188.pdf

Duality-invariant class of two-dimensional field theories

Correlation functions and vertex operators of Liouville theory

A causal Poisson bracket algebra for Liouville exponentials on a cylinder is derived using an exchange algebra for free fields describing the in and out asymptotics. The causal algebra involves an even number of spacetime points with a minimum of four. A quantum realization of the algebra is obtained which preserves causality and the local form of non-equal time brackets.

A causal algebra for Liouville exponentials

A causal Poisson bracket algebra for Liouville exponentials on a cylinder is derived using an exchange algebra for free fields describing the in and out asymptotics. The causal algebra involves an even number of space-time points with a minimum of four. A quantum realisation of the algebra is obtained which preserves causality and the local form of non-equal time brackets.

A Causal Algebra for Liouville Exponentials

We obtain the parity invariant generating functional for the canonical transformation mapping the Liouville theory into a free scalar field and explain how it is related to the pseudoscalar transformation

I. Sachs

Papers

On the Canonical Equivalence of Liouville and Free Fields