Structure of the three-dimensional quantum euclidean space

2000/04/03 by Bianca L. Cerchiai, B. L. Cerchiai, J. Madore +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Completeness (order theory) #Computer science #Euclidean geometry #Euclidean space #Geometry #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Space (punctuation) #hep-th #math-ph #math.MP #math.QA #msc:17B37 #msc:81R50

paper · pdf · doi:10.1007/s100520050013

published as Eur.Phys.J.C16:169-180,2000 · 22 pages, latex

arxiv created 2000/04/03 · openalex publication_date 2000/08/01 · arxiv updated 2011/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

As an example of a noncommutative space we discuss the quantum 3-dimensional Euclidean space R³_q together with its symmetry structure in great detail. The algebraic structure and the representation theory are clarified and discrete spectra for the coordinates are found. The q-deformed Legendre functions play a special role. A completeness relation is derived for these functions.

Citations

• The Hilbert Space Representations for SO_q(3)-symmetric quantum mechanics
• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Basic Hypergeometric Series
• Gauge theory on noncommutative spaces
• Quantization of Lie Groups and Lie Algebras

Cited by

• On the decoupling of the homogeneous and inhomogeneous parts in inhomogeneous quantum groups