1993/11/24 by Achim Kempf, A. Kempf · 410 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Classical mechanics #Fock space #Geometry #Group (periodic table) #Limiting #Mathematical physics #Mathematics #Momentum (technical analysis) #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Quantum #Quantum mechanics #Symmetry (geometry) #Theoretical physics #Uncertainty principle #hep-th
paper · pdf · doi:10.1063/1.530798
published in Journal of Mathematical Physics 35(9), 4483-4496 (American Institute of Physics) · 15 pages, Latex, preprint DAMTP/93-65
arxiv created 1993/11/24 · openalex publication_date 1994/09/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
The commutation relations, uncertainty relations, and spectra of position and momentum operators were studied within the framework of quantum group symmetric Heisenberg algebras and their (Bargmann) Fock representations. As an effect of the underlying noncommutative geometry, a length and a momentum scale appear, leading to the existence of nonzero minimal uncertainties in the positions and momenta. The usual quantum mechanical behavior is recovered as a limiting case for not too small and not too large distances and momenta.