Coherent State on SUq(2) Homogeneous Space

TL;DR

This paper thoroughly analyzes SU_q(2) coherent states, demonstrating their completeness, resolution of unity, and their role in representing the q-sphere, with implications for physical models and differential calculus on quantum spaces.

Contribution

It provides a detailed study of SU_q(2) coherent states, including their completeness, resolution of unity, and their application to the q-sphere, advancing understanding of quantum group coherent states.

Findings

SU_q(2) coherent states are complete and resolve the unity.

The q-sphere is represented in complex coordinates via these states.

High spin limit behavior of the coherent states is discussed.

Abstract

The generalized coherent states for quantum groups introduced by Jurco and Stovicek are studied for the simplest example SU_q(2) in full detail. It is shown that the normalized SU_q(2) coherent states enjoy the property of completeness, and allow a resolution of the unity. This feature is expected to play a key role in application of these coherent states in physical models. The homogeneous space of SU_q(2), i.e. the q-sphere of Podles, is reproduced in complex coordinates by using the coherent states. Differential calculus in the complex form on the homogeneous space is developed. High spin limit of the SU_q(2) coherent states is also discussed.