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Simple field theoretical models on noncommutative manifolds
H. Grosse, C. Klimcik, P. Presnajder
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…
Topologically nontrivial field configurations in noncommutative geometry
H. Grosse, C. Klimcik, P. Presnajder
In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserv…
Field Theory on a Supersymmetric Lattice
H. Grosse, C. Klimcik, P. Presnajder
A lattice-type regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integer-valued sequence of…
Towards Finite Quantum Field Theory in Non-Commutative Geometry
H. Grosse, C. Klimcik, P. Presnajder
We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symm…