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)

References in corpus (1)

• Towards Finite Quantum Field Theory in Non-Commutative Geometry

Cited by in corpus (7)

• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Brane Dynamics in Background Fluxes and Non-commutative Geometry
• Higher dimensional geometries related to fuzzy odd-dimensional spheres
• Open Strings and Non-commutative Geometry of Branes on Group Manifolds
• Noncommutative Geometry for Pedestrians
• Supersymmetry and Noncommutative Geometry
• Degeneracy and Para-supersymmetry of Dirac Hamiltonian in (2+1)- Spacetime