The \({\rbb Z}_{\mibs N}\) Symmetric Quantum Lattice Field Theory The Quantum Group Symmetry, the Yang–Baxter Equation, and the Integrals of Motion

Abstract

We study the quantum group symmetry of the \({\bb Z}_{N}\) symmetric lattice field theory, which is viewed as a discretization of the \(\widehat{s\ell (N)}\) affine Toda field theory. We reveal the quantum group structure, and construct explicitly the quantum local integrals of motion by use of the quantum dilogarithm function.