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Finite quantum field theory in noncommutative geometry. (English) Zbl 0846.58015
Summary: We describe a self-interacting scalar field on a truncated sphere and perform the quantization using the functional (path) integral approach. The theory possesses full symmetry with respect to the isometries of the sphere. We explicitly show that the model is finite and that \(UV\) regularization automatically takes place.

MSC:
58D30 Applications of manifolds of mappings to the sciences
81V15 Weak interaction in quantum theory
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
81T70 Quantization in field theory; cohomological methods
81T18 Feynman diagrams
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