Differential calculus and gauge theory on finite sets

Abstract

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 (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 which is related to q-calculus.

24 pages, LaTeX, GOET-TP 33/93, to appear in J. Phys. A: Math. Gen

References in corpus (2)

• Noncommutative Geometry and Gauge Theories on Discrete Groups
• Higgs Mass and Noncommutative Geometry

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