Simple field theoretical models on noncommutative manifolds

Abstract

We review recent progress in formulating two-dimensional models over noncommutative manifolds where the space-time coordinates enter in the formalism as non-commuting matrices. We describe the Fuzzy sphere and a way to approximate topological nontrivial configurations using matrix models. We obtain an ultraviolet cut off procedure, which respects the symmetries of the model. The treatment of spinors results from a supersymmetric formulation; our cut off procedure preserves even the supersymmetry.

15 pages, TeX (based on lectures given by H. Grosse at Workshops in Clausthal (Germany) and Razlog (Bulgaria) in August 1995)