Three short distance structures from quantum algebras

1997/09/15 by Achim Kempf, A. Kempf · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Geometry #Homogeneous space #Mathematics #Mechanism (biology) #Noncommutative and Quantum Gravity Theories #Observable #Physics #Pure mathematics #Quantum #Quantum mechanics #Theoretical physics #hep-th #math.QA #q-alg

paper · pdf · doi:10.1023/a:1022865313770

published in Czechoslovak Journal of Physics 47(12), 1191-1198 (Springer Science+Business Media) · 8 pages LaTeX2e, Proceedings 6th Coll. Quantum Groups and Integrable Systems, Prague 19-21 June '97

arxiv created 1997/09/15 · openalex publication_date 1997/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We review known and we present new results on three types of short distance structures of observables which typically appear in studies of quantum group related algebras. In particular, one of the short distance structures is shown to suggest a new mechanism for the introduction of internal symmetries.

Citations

• Gravitational quantum limit for length measurements
• The algebraic structure of the generalized uncertainty principle
• Uncertainty relation in quantum mechanics with quantum group symmetry
• On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
• String theory beyond the Planck scale
• QUANTUM GRAVITY AND MINIMUM LENGTH
• Minimal length uncertainty relation and ultraviolet regularization