63 research outputs found
Simple field theoretical models on noncommutative manifolds
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.Comment: 15 pages, TeX (based on lectures given by H. Grosse at Workshops in
Clausthal (Germany) and Razlog (Bulgaria) in August 1995
Field Theory on a Supersymmetric Lattice
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 finite dimensional rings of supermatrices and by
using the differencial calculus of non-commutative geometry. The regulated
theory involves only finite number of degrees of freedom and is manifestly
supersymmetric.Comment: 31 pages, LaTe
Towards Finite Quantum Field Theory in Non-Commutative Geometry
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 symmetry with respect to the isometries of the sphere.
We explicitely show that the model is finite and the UV-regularization
automatically takes place.Comment: 19 pages, LaTe
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