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Differential calculus and gauge theory on finite sets

A Dimakis and F Muller-Hoissen

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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.


PACS

11.15.-q Gauge field theories

02.30.-f Function theory, analysis

02.10.Yn Matrix theory

02.40.-k Geometry, differential geometry, and topology

02.10.Ab Logic and set theory

MSC

81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)

53Cxx Global differential geometry (See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx)

15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 9 (7 May 1994)



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