Normal ordering and quantum groups

Abstract

The irreducible R-matrices associated with the quantum Liouville and sine-Gordon equations were classified by the su(2) index l, 2l integer. We find that the associated quantum field theories must have the following equal time operator product expansions in the lattice approximation $${\text{e}}^{ + \eta \phi } \phi _{\text{r}} = \pm /(\eta /\Delta ){\text{ e}}^{ + \eta \phi } {\text{ + nonsingular operator}}$$ . The lattice L-operator is found to have the form exp ΦΔ, where Δ is the lattice interval and Φ is the obvious quantum analogue of the L-matrix of classical Liouville or sine-Gordon field theory.