Inhomogeneous quantum groups as symmetries of phonons

Abstract

The quantum-deformed (1+1) Poincar\'e algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from the quantum group structure. Inhomogeneous quantum groups are thus proposed as kinematical invariances of discrete systems.