Grosse, H.; Klimčík, C.; Prešnajder, P. Finite quantum field theory in noncommutative geometry. (English) Zbl 0846.58015 Int. J. Theor. Phys. 35, No. 2, 231-244 (1996). 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. Cited in 43 Documents 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 Keywords:noncommutative geometry; functional path integral; truncated sphere; quantization PDF BibTeX XML Cite \textit{H. Grosse} et al., Int. J. Theor. Phys. 35, No. 2, 231--244 (1996; Zbl 0846.58015) Full Text: DOI References: [1] Connes, A. (1986).Publications IHES,62, 257. [2] Connes, A. (1990).Géométrie Non-Commutative, Inter Editions, Paris. [3] Dubois-Violette, M. (1988).Comptes Rendus de l’Academie des Sciences Paris Serie I,307, 403. [4] Dubois-Violette, M., Kerner, R., and Madore, J. (1990).Journal of Mathematical Physics,31, 316. · Zbl 0704.53081 · doi:10.1063/1.528916 [5] Coquereaux, R., Esposito-Farese, G., and Vaillant, G. (1991).Nuclear Physics B,353, 689. · doi:10.1016/0550-3213(91)90323-P [6] Chamseddine, A. H., Felder, G., and Fröhlich, J. (1992). Gravity in the noncommutative geometry, Zürich preprint ETH-TH/1992-18. [7] Madore, J. (1991).Journal of Mathematical Physics,32, 332. · Zbl 0727.53084 · doi:10.1063/1.529418 [8] Madore, J. (1992).Classical and Quantum Gravity,9, 69. · Zbl 0742.53039 · doi:10.1088/0264-9381/9/1/008 [9] Madore, J. (n.d.).Non-Commutative Geometry and Applications, Cambridge University Press, Cambridge, to appear. · Zbl 0727.53084 [10] Grosse, H., and Prešnajder, P. (1993).Letters in Mathematical Physics,28, 239. · Zbl 0813.46065 · doi:10.1007/BF00745155 [11] Grosse, H., and Madore, J. (1992).Physics Letters B,283, 218. · doi:10.1016/0370-2693(92)90011-R [12] Grosse, H., Klimčík, C., and Prešnajder, P. (n.d.-a). Field theory on truncated superspace, to appear. [13] Grosse, H., Klimčík, C., and Prešnajder, P. (n.d.-b). Finite gauge model on truncated sphere, to appear. [14] Prudnikov, A. P., Brytshkov, Yu. A., and Maritshev, O. I. (1981).Integrals and Series, Nauka, Moscow [in Russian]. [15] Simon, B. (1974).The P(\(\Phi\))2 Euclidean (Quantum) Field Theory, Princeton University Press, Princeton, New Jersey. · Zbl 1175.81146 [16] Vilenkin, N. Ya. (1965).Special Functions and the Theory of Group Representations, Nauka, Moscow [in Russian]. · Zbl 0144.38003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.