1994/01/28 by Aristophanes Dimakis, A. Dimakis, Folkert Müller-Hoissen +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Calculus (dental) #Differential (mechanical device) #Differential calculus #Differential form #Gauge theory #Lattice gauge theory #Mathematical physics #Mathematics #Multivariable calculus #Physics #Pure mathematics #Quantum differential calculus #Time-scale calculus #hep-th
paper · pdf · doi:10.1088/0305-4470/27/9/028
published as J.Phys. A27 (1994) 3159-3178 · 24 pages, LaTeX, GOET-TP 33/93, to appear in J. Phys. A: Math. Gen
arxiv created 1994/01/28 · openalex publication_date 1994/05/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (1986) (which is an essential ingredient of his reformulation of the standard model of elementary particle physics) is recovered in our approach. Reductions of the universal differential calculus to 'lower-dimensional' differential calculi are considered. The 'complete reduction' leads to a differential calculus on a periodic lattice.