Inomogeneous Quantum Groups as Symmetries of Phonons

TL;DR

This paper demonstrates that inhomogeneous quantum groups serve as the symmetry framework for phonons in a harmonic chain, linking quantum group structures to discrete system invariances.

Contribution

It introduces inhomogeneous quantum groups as the symmetry of phonons in discrete systems, extending quantum group applications to condensed matter physics.

Findings

Quantum deformed Poincare algebra describes harmonic chain symmetries

Phonon processes derived from quantum group structures

Inhomogeneous quantum groups proposed as invariance of discrete systems

Abstract

The quantum deformed (1+1) Poincare' 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 invariance of discrete systems.