The Quantum Spheres and their Embedding into Quantum Minkowski Space-Time

TL;DR

This paper explores the embedding of Podle extquoteright s quantum spheres into quantum Minkowski space-time, revealing their structure as slices along the time coordinate and analyzing their transformation properties under quantum group actions.

Contribution

It demonstrates that quantum spheres can be viewed as time slices within quantum Minkowski space-time and analyzes their state transformations under quantum group coactions.

Findings

Quantum spheres are slices of quantum Minkowski space-time.

Transformed quantum sphere states decompose into orthogonal subspaces.

Quantum sphere states exhibit periodicity under group transformations.

Abstract

We recast the Podle\`s spheres in the noncommutative physics context by showing that they can be regarded as slices along the time coordinate of the different regions of the quantum Minkowski space-time. The investigation of the transformations of the quantum sphere states under the left coaction of the ${\cal SO}_{q}(3)$ group leads to a decomposition of the transformed Hilbert space states in terms of orthogonal subspaces exhibiting the periodicity of the quantum sphere states.