Poisson Lie Group Symmetries for the Isotropic Rotator

TL;DR

This paper introduces a novel Hamiltonian formulation of the classical isotropic rotator featuring Poisson Lie group symmetries, linking classical models to quantum group symmetries and exploring interactions between rotators.

Contribution

It presents a new Hamiltonian framework where $SU(2)$ symmetries are Poisson Lie group symmetries, extending the classical rotator model to include quantum group analogs.

Findings

Left and right $SU(2)$ transformations are Poisson Lie symmetries.

The formulation applies to systems of two interacting rotators.

Connections to quantum group symmetries are established.

Abstract

We find a new Hamiltonian formulation of the classical isotropic rotator where left and right $SU(2)$ transformations are not canonical symmetries but rather Poisson Lie group symmetries. The system corresponds to the classical analog of a quantum mechanical rotator which possesses quantum group symmetries. We also examine systems of two classical interacting rotators having Poisson Lie group symmetries.