On classical and quantum integrable field theories associated to Kac-Moody current algebras

Abstract

We present classical and quantum algebraic structures for two-dimensional integrable field theories associated to Kac-Moody current algebras. We obtain in particular classical and quantum discretized versions of such current algebras. The corresponding monodromy matrix is shown to satisfy extended quantum group relations, leading to integrable properties of these theories. We apply our constructions to the lattice non-abelian Toda field theory.