Coherent States, Dynamics and Semiclassical Limit on Quantum Groups

TL;DR

This paper constructs coherent states on the quantum group SU_q(2), explores their semiclassical limit as q approaches 1, and investigates the dynamics related to classical rotations within this quantum framework.

Contribution

It introduces a new approach to defining coherent states on quantum groups using harmonic analysis and representation theory, and connects q-deformation with contact geometry.

Findings

Coherent states on SU_q(2) are explicitly constructed.

Semiclassical limit q→1 is analyzed with emphasis on special states.

Dynamics on the quantum group relate to classical rotations.

Abstract

Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to $q$-deformation as a $q$-Weyl quantization and a relavence of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.