1994/01/19 by Markus J. Pflaum · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Fiber bundle #Fock space #Instanton #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Quantum #Quantum differential calculus #Quantum no-deleting theorem #Sheaf #Vector bundle #hep-th #math.QA
paper · pdf · doi:10.1007/bf02112317
published as Commun.Math.Phys.166:279-316,1994 · 50 pages
arxiv created 1994/01/19 · openalex publication_date 1994/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of quantum spaces noncommutative principal and vector bundles are defined and their properties are studied. Important constructions in the classical theory of principal fibre bundles like associated bundles and differential calculi are carried over to the quantum case. At the end q-deformed instanton models are introduced for every integral index.