1999/10/08 by J. Wess, Wess, J. · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.48550/arxiv.math-ph/9910013
63 pages, 2 figures, 38. Internationale Universitaetswochen fuer Kern- und Teilchenphysik, Schladming, Austria
arxiv created 1999/10/08 · openalex publication_date 1999/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate laws of physics based on this calculus. Then we realize that an interpretation of these laws is only possible if we study representations of the algebra and adopt the quantum mechanical scheme. It turns out that observables like position or momentum have discrete eigenvalues and thus space gets a lattice-like structure. In section 2 we study a framework for higher dimensional noncommutative spaces based on quantum groups. The Poincare-Birkhoff-Witt property and conjugation properties play an essential role there. In these spaces derivatives are introduced and based on these derivatives a q-deformed Heisenberg algebra can be constructed.