Differential calculus and gauge theory on finite sets
High Energy Physics - Theory
2009-10-28 v1
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.
Keywords
Cite
@article{arxiv.hep-th/9401149,
title = {Differential calculus and gauge theory on finite sets},
author = {A. Dimakis and F. M"uller-Hoissen},
journal= {arXiv preprint arXiv:hep-th/9401149},
year = {2009}
}
Comments
24 pages, LaTeX, GOET-TP 33/93, to appear in J. Phys. A: Math. Gen